
Book^ P-53 



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NATURAL PHILOSOPHY, 



FOR SCHOOLS, FAMILIES, AND PRIVATE STUDENTS. 



BY A. H. LINCOLN PHELPS, 

PRINCIPAL OF THE PATAPSCO FEMALE INSTITUTE, MARYLAND. % 

AUTHOR OF THE FIRESIDE FRIEND, &C. A SERIES OF WORKS ON BOTANY, NATURAL PHILOSOPHY 
AND CHEMISTRY, DESIGNED FOR BEGINNERS AND MORE ADVANCED STUDENTS. &C. 










NEW EDITION, REVISED AND CORRECTED. 



NEW YORK : 
PUBLISHED BY HUNTINGTON AND SAVAGE, 

216 PEARL STREET. 



m - - - - - A -— irrnmrTrniwniff 






Entered according to Act of Congress, in the year 1846, by 

HUNTINGTON & SAVAGE, 

In the Clerk's Office of the District Court of the United States for the 
Southern District of New-York. 



I 



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V- 



■ 



PREFACE 



This work, though based upon the labors of the learned, is not a mere com- 
pilation. — The author has endeavored to invest the subject with freshness and 
interest, to enliven the progress of the young, as they climb the hill of science. 
We have sometimes paused on our way, to discourse of Him who formed the 
world, and from whose eternal mind the laws of physical science originated. — 
Our hearts have been warmed and animated with thoughts of the wisdom and 
goodness which irradiate every page of the volume of nature. 

American parents and teachers ; to aid you in your duties, I have labored to 
prepare this volume. I commit it to you, in the confidence that while it shall 
impart to your children and pupils the principles of science, it will, at the same 
time, exert a salutary influence on their moral and religious affections. 

In the attempt made to connect religious sentiment with the study of the 
sciences, I find myself supported by that profound and philosophical writer, 
Madame Necker De Saussure, from whose second volume on Progressive Edu- 
cation, the following is an extract. " Religion alone unites and connects the 
various departments of education, external objects with the affections of the 
heart, the laws of physics with the laws of mind ; it is the influence of religion 
only which can cause science and duty to meet in the same point. What rela- 
tion, merely human, could we, for example, find between two subjects in ap- 
pearance so foreign from each other, as those of physical phenomena, and the 
moral obligations imposed on man ? and yet a connection exists ; they have 
one common source. One God, the sovereign legislator of nature and the soul, 
wills the reign of universal order. He has subjected matter to the laws of an 
irresistible necessity, and he has imposed on the free agent, man, a necessity 
which, though it appears less imperious, forces his will by bitter experience of the 
evils attached to a neglect of duty. When the creations, and laws of one dis- 
cerning mind, present themselves on every side, and in the government of the 
universe, numerous relations are seen to exist between the different departments 



IV PREFACE. 

of knowledge. To the subjects most fitted to exercise the talent of investigation 
inherent in the mind of man, are connected objects which appear chiefly fitted 
to his physical wants, and even those which seem created but to please his ima- 
gination. If God is the eternal geometrician, who has calculated with exacti- 
tude the measure of the different forces in the universe, if he is the wise legis- 
lator who has engraven his laws upon our souls, if he is the supreme artist, who 
has spread forth beauty upon the earth and in the heavens, and has rendered us 
sensible to its charms ; and as there is nothing in the physical world which is not 
the immediate work of God, and nothing in the moral world, which does not 
result from faculties with which he has endowed man, there can be neither 
object nor thought, which may not be connected with God. Thus all may be 
linked together, all may harmonize ; ideas, before insulated, unite in the mind 
of the pupil ; he views creation as a whole ; — and as soon as he perceives the 
unity of design in nature, his reason, though still feeble, presents some re- 
semblance to the Supreme reason which conceived the design" 

To Teachers, I would most solemnly affirm as the result of my experience 
in education, that the only effectual method of improving the characters of pupils 
is through the influence of religious truths; — and that intellectual culture may 
be so conducted as to lend most important aid in the great work of Christian 
Education, which should be the Alpha and Omega, the beginning and end 
of life. 



CONTENTS 



PART I. 



OF MATTER AND ITS MECHANICAL PROPERTIES. 

PAGE. 

LECTURE I. Introduction; the objects and advantages of Science, - 9 
" II. Of abstract Science. Departments of Natural Philoso- 

phy. Properties of Matter, ------- 14 

" III. Inertia. Attraction and Repulsion. Different kinds of 

Attraction, -----21 

« IV. Gravity, 25 

" V. Center of Gravity, 32 

" VI. Motion and Force. Laws of Motion, 40 

" VII. Compound Motion. Composition and Resolution of Forces, 50 

« VIII. Accelerated and Retarded Motion, 56 

" IX. Curvilinear Motion. Projectiles, --------61 



PART II. 



;ti 


JRE X. 


a 


XI. 


a 


XII. 


u 


XIII. 


« 


XIV. 


« 


XV. 


u 


XVI. 


it 


XVII 



OF THE MECHANICAL POWERS. 

Machines. The Cord. The Lever, -.-.-. 69 
The Lever continued, ----------73 

The Inclined Plane, - 80 

The Pulley, ----- 83 

The Wheel and Axle, The Wedge. The Screw, - 86 
Friction. Moving Powers. General Remarks upon 

Machinery, ----- - 93 

The Pendulum, ----- -------- 100 

Locomotion^ 104 

1* 



VI 



CONTENTS. 



LECTURE XVIII. 

XIX. 

XX. 

XXI. 



PART III. 
HYDROSTATICS. 

PAGE. 

Mechanical Properties of Liquids, - - - - - 109 

Pressure of Liquids, ----------112 

Specific Gravity, ---------- 122 

Liquids in Motion, or Hydraulics, ----- 129 



LECTURE XXII. 


<< 


XXIII. 


« 


XXIV. 


it 


XXV. 


u 


XXVI. 


tt 


XXVII. 



PART IV. 
PNEUMATICS. 

jEriform Bodies. Atmosphere. The Air-pump, - 132 
Properties of Air, ---------- 138 

The Condensation of Air. Condensing Syringe. 

Artificial Fountains. Air-Gun. Diving-Bell, 144 
Barometer. Effect of Heat upon Air, - - - - 149 
Winds — Their Causes and Effects, ----- 155 
Meteorology. Steam. Elastic Force of Steam. 

Steam Engine, ---------- 159 

" XXVIII. Atmospheric Pressure upon Water. Pumps. Syphons, 165 

PART V. 
ACOUSTICS. 

LECTURE XXIX. Sonorous Bodies. Bells. Musical Strings. ^Eolian 

Harp, 170 

" XXX. Medium of Sound. The Ear. Echo. Speaking 

Trumpet. Velocity of Sound. Music. The 
Human Voice, ---------- 175 



LECTURE XXXI 



XXXIII. 
XXXIV. 



PART VI. 
OPTICS. 

Light. Definitions. Motion of Light. Its Inten- 
sity. Of Reflection and Refraction, - - - 186 
XXXII. Reflection from Mirrors. Plane Mirrors. Convex 

Mirrors. Concave Mirrors, - - - - - - 191 

Refraction of Light, - - 205 

Lenses, ------ 215 



LECTURE XXXV. 



XXXVI. 



XXXVII. 



CONTENTS. Vii 

FAOl. 

Visual Angle. Fore- Shortening. Perspective. In- 
tensity of Light and Shade. Convergence of 
the Optic Axes, 222 

Duration of Impressions upon the Eye. Single 
Vision. Imperfection of Vision. Optical In- 
struments. Shadow, --------231 

Nature of Light. Decomposition of Light. Dis- 
persion of Light. Rain-bow. Absorption of 
Light, 243 



PART VII. 
ELECTRICITY AND MAGNETISM. 

LECTURE XXXVIII. Theories of Electricity. Mode of obtaining it. 
Conductors and Non-conductors. Atmos- 
pheric Electricity, -------- 252 

« XXXIX. Magnetism. Dip of the Magnet. Deviation of 

the Compass. Theory of Magnetism. The 
Compass, -- --------- 265 



PART VIII. 
CELESTIAL MECHANICS, OR ASTRONOMY. 

LECTURE XL. Introductory Remarks. Armillary Sphere. The Solar 
System. Planets. Comets. Application of Me- 
chanical Laws to Planetary Motion, - - - - 273 
" XLI. Fixed Stars. Constellations. Galaxy. Nebula?. Con- 

cluding Remarks, --------..- 286 



Note. — The matter in small type may be omitted by younger pupils, or at 
the first going over with the work, as also at public examinations. 



FAMILIAR LECTURES 

ON 

NATURAL PHILOSOPHY. 

PART I. 

OF MATTER AND ITS MECHANICAL PROPERTIES. 

LECTURE I. 

INTRODUCTION. 

OF THE OBJECTS AND ADVANTAGES OF SCIENCE. 

1. Natural Philosophy, recommends itself to attention both 
for its influence on the mind, and for its practical utility. 

2. The habit of study is of great importance. No one can 
ever arrive at eminence, or indeed be well prepared for the ordi- 
nary duties of life, who cannot fix his mind steadily upon a sub- 
ject, and follow out a train of reasoning. Such studies as require 
close reasoning, and consecutive thinking, are to be recommended 
for their influence on the mind, apart from their other advantages. 
Among this class of studies, none holds a higher rank than Natural 
Philosophy. Every young person should seek to apply himself to 
such pursuits as will strengthen his mind and invigorate his under- 
standing. If he would have his mental faculties bright and active, 
he must use them. 

3. The love of knowledge is a principle of our nature. To feel 
ourselves becoming wiser, more assimilated to the great minds 
which have instructed mankind, and better able to see the plan 
and harmony of the creation, seems to add dignity to our own 
minds. There are, in such feelings and perceptions, enjoyments 

1. Two recommendations of the study of Natural Philosophy. 

2. Habit of study. Why Natural Philosophy is useful in its effects on the 
mind. 

3. Dignity and Pleasures of knowledge. 



10 NATURAL PHILOSOPHY. 

which may be vainly sought, in amusements that neither elevate 
nor refine our nature. " He who is accustomed to trace the oper- 
ation of general causes, and the exemplification of general laws," 
says Herschel, " walks in the midst of wonders unknown to the 
ignorant, and unseen by the uninquiring eye ; every object that 
fails in his way elucidates some principle, affords some instruc- 
tion, and impresses him with a sense of harmony and order. Nor 
is it a mere passive pleasure which is thus communicated. A 
thousand questions are continually arising in his mind, a thousand 
subjects of inquiry presenting themselves, which keep his faculties 
in constant exercise, and his thoughts perpetually on the wing, so 
that lassitude is excluded from his life ; and that craving after arti- 
ficial excitement and dissipation of mind, which leads so many 
into frivolous, unworthy and destructive pursuits, is altogether 
eradicated from his bosom." 

4. Knowledge is power. It is this that gives to civilized man 
his advantage over the savage. It is knowledge which guides the 
arts that minister to the comforts of domestic life, directs the me- 
chanic in the fabrication of articles of convenience and luxury, and 
presides over the operations of war. It has been said, that " if a 
man have but a pot to boil, he may learn from science, lessons that 
will enable him to cook his morsel better, save his fuel, and both 
vary his dish and improve it." A knowledge of the principles of 
science, not only renders the man who labors for his bread more 
skilful and expert in his occupation, but gives him an opportunity 
while making improvements in the arts, to make new discoveries 
in Philosophy. 

5. The study of nature leads us to a more intimate communion 
with the Great Author of Nature. We follow his footsteps, we 
behold the works of his hand, and we learn the laws by which 
he governs the material world. What pursuit can be more noble, 
what better fitted to engage the attention and delight the heart 
of the philosopher and christian ? 

6. The term Philosophy means a knowledge of the reasons, or 
causes of things. A knowledge of these causes leads to important 
inventions. Every one is familiar with the fact, that the lid of a 
tea-kettle is forced upward when water is boiling violently within : 
yet, some grow old without ever thinking why this takes place. — 
An observing mind, while reflecting upon it, would perceive that 
water acted upon by heat passes into steam or vapor, and that 
the latter by its expansive force, raises the lid of the kettle. 

4. Power derived from knowledge. 

5. To what does the study of Nature lead ? 

6. Meaning of the term, Philosophy. Steps by which inventions are 
made. 



INTRODUCTION. 11 

Having ascertained this power of steam, he might then imagine 
how it could be applied to machinery, and thus proceed to invent 
a steam engine. By similar steps have those proceeded who 
have subjected the powers of nature to the control of man, and, by 
thus contributing to the comfort and prosperity of society, have 
enrolled their names among its benefactors. 

7. The term, Philosophy of Nature, usually called Natural 
Science, has an extended signification, including Chemistry which 
considers the elements of substances, and Natural History which 
observes their forms and external organs. 

8. Chemistry and Natural Philosophy may be considered as 
bearing a similar relation to each other as do the microscope and 
telescope ; the former looks at objects near by and scrutinizes 
their minutest parts ; while the latter takes a more general sur- 
vey and operates upon a much broader scale. 

9. Some knowledge of all the Natural Sciences is of great 
importance to the young. Attainments in any one, must facilitate 
the study of the others. In the study of Natural Philosophy, 
besides the advantages which may be expected in cultivating 
the powers of memory, reasoning, and observation, the mind is 
enlarged by new views of that Infinite Wisdom which has so 
nicely balanced the powers of nature, that all material things, 
whether atoms, systems, or worlds, are retained in their proper 
places, even by the very action of forces which tend to draw them 
in opposite directions. 

10. The Almighty Creator has brought into existence two very 
different classes of substances, mind and matter. Every thing 
we know, or of which we can conceive, belongs to one or the 
other of these great divisions. There must be one Being in 
the universe who has always existed, because neither mind nor 
matter could have created itself. This self-existent, uncreated 
Being, the Author of all things, is God. In our own persons, 
mind and matter are connected by a common tie which we call 
life. The brute creation have a lower order of mind called in- 
stinct, by means of which they accomplish their distinct ends. 
Plants have a living principle but are incapable of action. 
Stones, wood, water, and air, are matter uncombined with mind ; 
they have neither soul nor instincts, and possess no principle of life. 

11. Natural Philosophy is the study of matter with respect to 
its general properties and the laws by which it is governed. 

7. Difference between the Philosophy of Nature and Natural Philosophy. 

8. Natural Philosophy and Chemistry compared. 

9. Importance of all the Natural Sciences. 

10. Mind and Matter. Argument for the existence of Deity. Life. In- 
stinct. Inanimate objects. 

11. What is Natural Philosophy? 



12 NATURAL PHILOSOPHY. 

12. This science is founded on observation and experiment ; that 
is, it admits no principle which is not the result of careful and 
attentive observation, and which may not be tested by actual ex- 
periment. 

13. Matter is the subject of the science, and mind the instru- 
ment by which its operations are carried on. By means of the 
senses, which are, themselves, subject to the will of the soul or 
mind, the latter becomes acquainted with objects external to 
itself. 

14. We may then define matter to be that which acts upon any 
of our senses, either immediately, or by means of its effects on 
other bodies. Each of the senses gives information of certain 
properties of matter, the existence of which we could never have 
learned from any other source. 

To the sense of touch or feeling, we owe our ideas of the softness or hard- 
ness, and the length and breadth of bodies. Sight gives us ideas of color; 
without this sense we could have no conception of the effects of light, as seen 
in a picture, rainbow or cloud. We might, from feeling, learn to distinguish 
a square from a sphere or a cylinder, and acquire general notions of figure 
and extension, but could never have any idea of the variety of forms which 
are presented in a natural landscape, where rocks, trees, brooks and mead- 
ows are grouped together in a picturesque assemblage. A blind person 
might, by feeling, gain some idea of the magnitude and figure of a church, 
but he could have no conception of the beauty of architectural proportion. 

15. When, on entering an apartment, or walking in a garden, 
we perceive the odor peculiar to a rose, we believe this flower to 
be near us. When we hear a flute or a gun, w r e believe in the 
existence of an instrument which caused the sound, and should any 
one tell us that the odor or sound proceeded from nothing, we 
should know this to be false. 

16. The cause of all our various sensations we call matter. Our 
reference of the sensations to its cause, we call perception. 

17. The properties, and not the essence of matter, are the pro- 
per objects of philosophical inquiry : — thus, suppose one inquires 
what is an orange ? we answer it is something which is of a 
round figure, a yellow color, has an agreeable odor, and pleasant 
taste ; — but we have enumerated only qualities or properties of the 
orange ; and though we might go on and mention how it grew 
from a seed, and explain the whole process of vegetation, still we 
should not have answered the original question, ' what is an orange?' 



12. On what is Natural Philosophy founded? 

13. How does the mind learn the properties of matter ? 

14. Definition of matter. Touch. Sight. 

15. Smell and hearing. 

16. Perception. 

17. What are the proper objects of philosophical inquiry ? 



INTRODUCTION. 13 

if we consider this as referring to its essence. Such inqui- 
ries are beyond the limits of our faculties ; though in past ages 
they were vainly pursued by philosophers, who sought rather to 
perplex men by hypotheses, than to enlighten them by actual dis- 
coveries of truth. 

18. It is now admitted that mankind must be satisfied with 
making the best possible use of such knowledge of matter as 
they can gain by their senses, without attempting to form theories 
upon subjects beyond their reach, or " to draw on their imagina- 
tion for facts." 

19. The soul within its dark prison can look out upon external 
things only through those few avenues, the senses, which we must 
suppose reveal to us but a small part of the creation. Were a 
sense of discerning spiritual existences imparted to us, in what a 
new creation should we seem to exist ! 

20. But limited as human faculties are in this threshold of ex- 
istence, they can yet accomplish much by observing, comparing, 
and experimenting upon such properties of objects as they have 
the power to perceive. Thus the blind could not, by any expedi- 
ent, be made to see the forms of letters impressed upon the printed 
page, and it would be useless labor to attempt to teach them to 
read in this manner ; but by means of raised characters which 
they can learn to distinguish by touch, they may be instructed. 
Wherein then our Creator has withheld from us light, let us hum- 
bly acquiesce in our blindness, while we honor him, and promote 
our happiness, by making the best possible use of the faculties 
with which he has endowed us. 

21. In the beautiful language of an English writer,* " the character of the 
true philosopher is to hope all things not impossible, and to believe all 
things not improbable. He who has seen obscurities which appeared im- 
penetrable, in physical and mathematical science suddenly dispelled, and 
the most barren and unpromising fields of inquiry converted, as if by 
inspiration, into rich and inexhaustible springs of knowledge and power, 
on a simple change of view, or by merely bringing to bear on them 
some principle which it never occurred before to try, will surely be the 
very last to acquiesce in any dispiriting prospects of either the present 
or future destinies of mankind ; while, on the other hand, the boundless 
views of intellectual and moral, as well as material relations, which open 
to him on all sides in the course of these pursuits, the knowledge of the 
trivial place he occupies in the scale of creation, and the sense of his 
own weakness and incapacity to suspend or modify the slightest move- 

* Sir John Herschel. 

18. What is now admitted with respect to a knowledge of matter ? 
1.9. How can the soul gain any knowledge of external things ? Is it pro- 
bable that the senses reveal all which surrounds us ? 

20. Our limited faculties no excuse for mental inactivity. 

21. Character of the true philosopher. Importance of all natural objects 
to the philosopher. o 



14 NATURAL PHILOSOPHY. 

tnent of the vast machinery he sees in action around him, effectually con- 
vinces him that humility of pretension, no less than confidence of hope, is 
what best becomes his character. To the natural philosopher, there is no 
natural object trifling or unimportant. From the least of nature's works he 
may learn the greatest lessons. The fall of an apple to the ground may raise 
his thoughts to the laws which govern the revolutions of the planets in their 
orbits ; or the situation of a pebble may afford him evidence of the state of 
the globe before his species became its denizens. And this is, in fact, one 
of the great sources 01 delight which the study of natural science imparts 
to its votaries. A mind which has once imbibed a taste for scientific inquiry, 
and has learnt the habit of applying its principles readily to the cases which 
occur, has within itself an inexhaustible source of pure and exciting contem- 
plations ; such a man finds ' tongues in trees, books in the running brooks, 
sermons in stones, and good in everything.' " 



LECTURE II. 

OF ABSTRACT SCIENCE. DEPARTMENTS OP NATURAL 

PHILOSOPHY. PROPERTIES OF MATTER. 

22. Natural science is the knowledge of things, of causes and 
their effects ; or, in other words, of the laws of nature. Abstract 
science is the knowledge of signs as in language, or of numbers, 
as in arithmetic or algebra. It is also the study of independent 
truths which relate to space and extension, as in geometry and 
all subjects capable of accurate demonstration. 

23. Some acquaintance with the power of language is neces- 
sary towards the comprehension of any science ; and the more 
thorough and extensive is a knowledge of words or the signs 
used to convey ideas, the more readily can a person comprehend 
the teachings of others, and the more easily and accurately com- 
municate the results of his own inquiries. 

24. The learner in Natural Philosophy should have some ac- 
quaintance also with the elementary principles of mathematics, 
the knowledge of whose truths depends on reasoning rather than 
observation. Thus, when we see a triangle marked out before us, 
and it is demonstrated by a train of geometrical reasoning, thai 
the sum of the three angles is equal to two right angles, we are 
as perfectly certain of the fact as if it had been proved by actual 
measurement. 

22. Difference between Natural and Abstract science. 

23. Importance of understanding the power of language. 

24. On what do mathematical truths depend ? 



ABSTRACT SCIENCE. 15 

25. Upon a few simple truths involving space and numbers is 
built the noble science of Mathematics. Beginning with these 
truths, Euclid, more than two thousand years ago, erected, from 
materials furnished by his own reason, a system of geometry 
which succeeding mathematicians have neither been able to over- 
throw nor improve. Ancient philosophers thought they might, in 
the same abstract, independent manner, by the mere strength of 
their own reasoning, establish systems of Natural and Mental Phi- 
losophy. But it was soon found that the human mind could never 
ascertain by any effort of mere reasoning, that sugar would be 
dissolved by water, or marble remain unchanged in the same 
liquid. 

26. The progress of the physical sciences was long obstructed 
by the blindness of the learned to the true mode of scientific in- 
vestigations. As soon as philosophers began to understand that 
the only way of learning the laws of nature is to observe natural 
phenomena, and, consequently, began to substitute inquiry for hy- 
pothesis, discoveries were made and principles established. 

27. The science of Natural Philosophy is intimately connected 
with Mathematical Science ; and though we may not, in teaching 
the former, make use of mathematical demonstrations, they are the 
foundation on which depend many of the principles of philosophy. 

28. The particular branch of geometry called trigonometry,* 
enables the astronomer to use the earth as a base wherewith to 
measure the magnitude and distances of the sun and planets : it 
also enables the navigator on the broad ocean, to ascertain by ob- 
servations of the stars his exact position on the earth's surface. 
In determining the heights of mountains and buildings, and in the 
operations of the surveyor, the science of trigonometry is equally 
important. 

29. The annexed diagram shows some of the most 
important geometrical lines and figures. A c is the 
diameter of the circle OPM; B, a radius ; C, a 
chord; D, an arc; E, a tangent; F, a secant; G, a 
co-tangent ; H, the sine of the arc ab ; I, the cosine ; 
}{, the versed sine; L, the sine of the arc b O. The 
P| ■ *- ■ ^ — V I ^[ — K. C sine of an arc or angle is the perpendicular line drawn 
from the extremity of an arc O b, to the diameter 
of a circle, as H ; I is called the co-sine, and K the 
versed sine; L is the sine of complemental arc O b. 

* From the Greek trigonon and metreo, signifying to measure triangles. 

25. On what did Euclid erect his system of geometry ? 

26. What obstructed the progress of the physical sciences? 

27. Connection of Natural Philosophy with Mathematical Science. 

28. Uses of trigonometry. 

29. Explain the diagram of geometrical lines and figures. 




16 NATURAL PHILOSOPHY. 



DIVISIONS OF NATURAL PHILOSOPHY. 

30. Natural philosophy is divided into Mechanics or the mechan- 
ical properties of matter and the doctrine of equilibrium and mo- 
tion as respects solids ; Hydrostatics, relating to the equilibrium 
and motion of liquids ; Pneumatics, or the effect of forces on air 
and other gaseous fluids ; Acoustics, or the science of sound ; 
Optics, the science which treats of light and vision. To these 
may be added Electro-Magnetism and Astronomy. 



mechanics. 
Essential Properties of Matter. 

31. The two essential properties of matter, are extension and 
impenetrability. All matter of which we have any knowledge, 
exists in masses called bodies. 

32. All material substances have extension in length, breadth 
and thickness, and these constitute the dimensions of a body. 
Even the air which encompasses the globe is a body and has its 
dimensions ; — a river has its length, breadth and depth. The 
terms height, depth, and thickness, all mean the same thing al- 
though we apply them differently. When we measure from the 
base upward, we call this dimension, height ; thus we say the 
height of a mountain ; when we measure from the surface down- 
ward, we say depth, as of a river ; — thickness is not applied to 
water or gasses, but to solids only, as the thickness of ice, of a 
stratum of rock, &c. Width is also synonymous with breadth. 

33. The extension of a body, or that space which it occupies, is 
called its volume, and the quantity of matter which it contains, its 
mass. A portion of space which is destitute of matter, is called a 
vacuum. 

34. The limits of extension are called figure or shape. The 
productions of nature are seldom bounded by straight lines, thus 
animals and vegetables exhibit beautiful curves, and a graceful 
irregularity. Rocks and mountains have no determinate forms, 
and the masses which compose them are also irregular. Crystals 
present regular geometrical figures, each mineral substance pos- 

30. What are the departments into which Natural Philosophy may be 
divided. 

31. Which are the two essential properties of matter ? 

32. What constitute the dimensions of a body ? 

33. Volume, mass, vacuum. 

34. Figure, or shape. 






PROPERTIES OF MATTER. 17 

sessing, its own peculiar form of crystal, as each species of plant 
has its own form of leaf. 

35. By impenetrability is meant that property which a body 
has of occupying a certain space, and of excluding all other mat- 
ter from the space it occupies ; otherwise, any space might con- 
tain an indefinite quantity of matter, and bodies instead of resisting, 
would pass through each other, which is contrary to our daily ex- 
perience. 

36. Air and water are bodies ; we can no more penetrate the 
particles which compose these substances than those of a board 
or a piece of iron. In moving the hand through the air, we do 
not penetrate its particles, but they make way on each side. If 
the hand is plunged into a vessel filled with water, a quantity, 
equal in bulk to the hand, will flow out. The particles whicli 
compose air and water move freely, and are therefore easily 
separated from one another. 

37. In solid substances, such as wood and metals, the particles 
are less easily separated ; but a nail may be driven into the one, 
and a rivet drilled through the other ; in common language 
they are said to be penetrated by the nail or rivet ; but, in these 
cases, there is also a displacing of the particles which are crowded 
more closely, in order to make way for the harder bodies forcibly 
introduced. 

38. This property in bodies may be considered as the main- 
spring of all mechanical science. It is impenetrability which 
gives the force necessary to motion, affording to the sails of ves- 
sels, the oars of boats, the wheels of mills, and various kinds of 
machinery, a resistance in air and water, without which hu- 
man invention would be unavailing. 

We can form no notion of matter that has not extension, or 
dimensions, or that does not occupy space, in other words that is 
not impenetrable ; therefore we consider extension and impene- 
trability as essential properties of bodies. 

Properties of Matter not considered Essential, 

39. Divisibility was long classed among the essential proper- 
ties of matter, but in the present state of science, we cannot con- 
sider it as such. By divisibility is meant, that we can never di- 
vide a substance into parts so minute, that it may not be again 

35. Impenetrability. 

36. Impenetrabilty of air and water. 

37. Does a nail or rivet penetrate the particles of wood or iron 1 

38. Importance of impenetrability in mechanics. 

39. Is divisibility an essential property of matter 1 Examples of extreme 
divisibility of matter. «* 



18 NATURAL PHILOSOPHY. 

divided ; thus, it has been asserted, that matter is infinitely divis- 
ible. In proof of this opinion, it is said that any particle of matter 
must have an upper and under side ; every whole must have two 
halves, four quarters, &c* The extreme minuteness of division 
of which some substances are capable, is considered a proof oi 
this infinite divisibility of matter. We know that a single odorif- 
erous flower will perfume a large apartment ; the odor which 
passing from it, comes in contact with our organs of smell, is, 
in fact, particles of the flower itself; but though it may continue 
for many days to diffuse perfume, its substance does not seem at 
all lessened by the loss of these particles. A small bottle of per- 
fume will, for years, continue to diffuse odor, without any apparent 
diminution of its substance. The dust obtained by pounding a 
crystal, when examined with a microscope, presents the same 
form and angles which distinguished the mass ; and this dust is 
capable of farther subdivision with instruments sufficiently delicate. 

40. The microscope reveals, in the fine powder upon the out- 
side of a fig, animalcules, which, though, in reality, so small that 
many thousands might stand upon the point of a fine needle, ap- 
pear like droves of pigs, each, with limbs and the various organs 
necessary to carry on the functions of animal life. 

Suppose that an instrument should be constructed, (and the sup- 
position is not absurd,) which, in its magnifying powers, should 
exceed any microscope now known, as much as that does the un- 
assisted powers of the eye ; what new wonders might be revealed 
to us and what new proofs given of the divisibility of matter ! But 
examples showing that matter is divisible to a wondeiful extent, 
do not prove that there may not be ultimate particles which can- 
not be divided. 

* Although it may be impossible, by means of mechanical subdivision, as 
pounding, grinding, &c. to arrive at the ultimate atoms of bodies, yet chem- 
ical decomposition can effect what mechanical means cannot. 



40. Discoveries of the great divisibility of matter by means of the micro- 
scope. 



OF THE PROPERTIES OF MATTER. 



19 




41. Geometry teaches that space is 
infinitely divisible. In this science 
it is taken for granted, that a line, 
however small, may be divided. It 
may be demonstrated that the line 
a i is capable of being divided into 
any number of equal parts. Draw 
a line A I, parallel to a i, of any 
length, and at any distance you 
please, and divide it into as many 
equal parts, A B, B C, &c. as there 
are to be divisions in the smaller 
given line, say eight. Now, through 
the extremities A a, and I i draw 
the straight lines A a O and I i O, 
till they meet in the point O ; and 
from O, draw to the points of divi- 
sion B, C, D, E, &c. the straight 
lines O B, O C, &c. which shall like- 
wise divide the smaller line into 
eight equal parts. This operation, 
mathematically speaking, may be 
performed, however small the given 
line a i, and however great the num- 
ber of parts into which we may propose to divide it; though, in executing 
geometrical figures the lines may touch each other and lose their distinct- 
ness, as may be seen near the point O, because lines which we draw have 
some breadth. Thus, physically, this proposition is not true, though, mathe- 
matically speaking, there is no line, however small, which may not be again 
divided. 

42. But space is not matter, therefore if its infinite divisibility were de- 
monstrated, this would not prove the infinite divisibility of matter. Though 
Philosophy has not been able to determine this subject, Chemistry, a sister 
science, comes to our aid, and informs us that, by the analysis of bodies, she 
has discovered that they are composed of atoms * or particles which cannot 
be again divided.\ 

43. Porosity is a property which is found to exist in an in- 
verse proportion to density. The pores or interstices of sponge 
are filled with air. Put the sponge in water, and air will escape 

* The word atoms is from the Greek, and signifies that which cannot be 
further cut or divided. 

t Although in late works on Natural Philosophy, divisibility has been in- 
sisted on as an essential property of matter, the doctrine of atoms, or indivi- 
sible particles is by no means modern. Sir Isaac Newton says, " all things 
considered, it seems probable that God in the beginning, formed matter in 
solid, massy, hard, impenetrable, moveable particles, of such sizes and figures, 
and with such other properties, and in such proportion to space as most con- 
duced to the end for which he formed them." 



41. Space proved by geometry to be infinitely divisible. 

42. If it were proved that space is infinitely divisible, would this argu- 
ment apply to matter ? How has the existence of ultimate atoms been 
proved ? 

43. What is meant by porosity, and in what substances does it exist ? 



20 NATURAL PHILOSOPHY. 

in little bubbles and give place to water. Wood and even metals 
are porous, though the pores are less visible than in sponge and 
light bread. Oil spilled upon an oaken or pine floor is absorbed 
by pores in the wood ; by the application of substances, such as soap 
or lye, which unite with the oil and change its nature, its effects 
are destroyed. Metals formed into thin globes and filled with 
liquid, on being subjected to powerful pressure have exhibited 
their outer surface covered with moisture exuded through the 
pores. The diamond, the hardest of all known substances, admits 
the passage of light. As matter is impenetrable, we must con- 
sider this, and all other cases of transparency as owing to the po- 
rosity of the substance. 

44. Density is closeness of texture. Bodies are heavy in pro- 
portion as they are dense. In two bodies of equal bulk, that is 
most dense which weighs most. Sponge is less dense than wood, 
and wood is less dense than iron. The metals vary in their de- 
grees of density ; platina is more dense than gold, and gold is 
more dense than silver. Any body can be made more dense by 
bringing its particles into a more compact state, by hammering, 
pressure, &c. 

45. Compressibility is owing to the porosity of matter. All 
known substances are capable of being made to occupy less space, 
by forcing the particles which compose them into closer contigui- 
ty. The more dense a substance is, the less it is compressible. 
Hardness and softness are terms which, in common language, sig- 
nify the same properties as density and compressibility. 

46. Expansion is that property of matter whereby the particles 
which compose a body are divided to a great distance, and thus 
occupy more space than in their ordinary state. 

47. Elasticity is that property by which a body after being 
compressed, returns to its original form on the removal of the com- 
pressing force. Elastic bodies, as ivory, marble and steel, when 
thrown against any hard substance, rebound; but non-elastic 
bodies, as wet-clay, dough, putty, &c, adhere to the substances 
on which they fall, and do not return to their former shape. 

Gravity and Inertia are properties of matter which are inti- 
mately connected with the laws of motion. 

44. Why are some bodies heavier than others? What property is the 
opposite of porosity ? Density of metals. 

45. Compressibility. 

46. Expansion. 

47. Elasticity. Gravity and Inertia. 



OF THE PROPERTIES OF MATTER. 21 



LECTURE III. 

INERTIA. ATTRACTION AND REPULSION. DIFFERENT 

KINDS OF ATTRACTION. 



Inertia, 



48. Inertia is a property of matter by which it resists any 
change of state, whether of rest or motion. Matter is inactive, it 
has neither the power to move, nor to stop its own motion. The 
term inertia was introduced into Philosophy by those who maintain- 
ed that all bodies have a propensity to rest. They considered matter 
as somewhat resembling indolent persons, who prefer rest to exer- 
tion, ascribing to bodies a dislike to motion, similar to that which 
sluggards have for labor. This opinion was founded on a false 
view of the nature of matter which requires as much force to put 
it in a state of rest as of motion. 

49. Matter does not move itself; a stone, for example, never 
raises itself from the ground, nor, without some external force, 
moves in any direction. A stone thrown from the hand, after 
moving for a time, at length falls to the earth, and its motion 
ceases. It may be asked, "does not this prove that the stone has a 
tendency to rest, rather than motion ?" We answer, that force 
is equally necessary in the one case as in the other, although the 
exertion of it is not equally apparent in both cases. We see the 
force which impels the stone, but cannot see that which stops its 
motion. 

50. The resistance of air impedes the motion of bodies ; and 
besides this, there is, constantly in operation, a powerful force, 
called the attraction of gravitation^ which tends to bring to the 
earth all substances within its sphere of action. 

51 . A top whirled from the hand spins swiftly at first, but grad- 
ually moves more slowly, until its motion ceases, and it rests upon 
the floor. The friction, or rubbing against the floor, the resist- 
ance of the air, and the attraction of gravitation, are the united 

48. Define inertia. Has matter any power to move, or to stop its own 
motion ? What was the origin of the term inertia 1 

49. Force as necessary to stop motion, as to produce it. 

50. What forces tend to destroy upward motion ? 

51. What three forces tend to bring a whirling top to a state of rest ? 



22 NATURAL PHILOSOPHY. 

forces which stop the motion of the top ; or, by their continued 
operation, at length overcome the impulse at first given by the 
force of the hand. 

52. The inertia of a body is proportional to its quantity of mat- 
ter or weight. 

Attraction and Repulsion. 

53. There are, in nature, two opposite powers, attraction and 
repulsion ; the former tends to bring the particles of matter togeth- 
er, the latter to drive them asunder. These powers, by the Crea- 
tor and Governor of the universe, are made to balance each other ; 
were it otherwise, disorder and ruin would prevail in the material 
world. 

54. Should attraction reign uncontrolled, the particles which 
compose bodies would rush together into close contact. Accord- 
ing to the suggestion of some philosophers, our globe and all that 
it contains might be compressed to the size of an apple. It is a 
familiar fact that nearly two thousand gallons of steam may be 
condensed to one gallon of water. 

55. Repulsion, operating without any check from attraction, 
would destroy the solidity of all bodies on the earth, and even the 
earth itself; which, in that case, would exist only in the form of 
the most rarefied gas. The burning of a log of wood shows a 
solid body passing off in vapor, since all that remains solid is a 
small quantity of ashes bearing but a very small proportion to 
the size of the wood. 

56. The great agent in repulsion, is the principle of heat, 
called caloric, the consideration of which belongs to Chemistry. 

Cohesive Attraction. 

57. The attraction of cohesion is the force which keeps the 
particles of matter together, forming distinct bodies. It acts 
only at insensible distances. * The table, the iron stove and look- 
ing glass are composed of very small particles of matter, held to- 
gether by the power of cohesion. On attempting to separate a 
solid body, we perceive that it is held together by a power which 

52. To what is inertia proportional ? 

53. What two opposite powers in nature ? 

54. Effects of uncontrolled attraction. 

55. Of repulsion. 

56. The great agent in repulsion. 

57. Attraction of cohesion. What is necessary towards cohesive attrac- 
tion ? What would be the effect if this power were to cease ? 



OP THE PROPERTIES OF MATTER. 23 

requires more or less resistance to overcome. This is cohesive, 
sometimes called adhesive attraction. 

If two flat peices of lead, with smooth surfaces, be brought to- 
gether, they will be held in contact by a powerful force. Two 
plates of glass when placed together will cohere so strongly as 
not to be easily separated. 

58. Liquids are less influenced than solids by cohesive attrac- 
tion. In drops of dew suspended from the leaves of plants we 
see the operation of this power, both in the globular form which 
the particles of moisture assume, and in their remaining attached 
to the leaf. If small globules of mercury are placed upon a plate 
of glass or other smooth substance, they will move towards each 
other and unite. In order that this should take place, the globules 
of mercury must be brought within the sphere of their mutual at- 
traction. Liquids, in common language, are said to be thick or 
thin according as their cohesive attraction is more or less power- 
ful ; but dense and rare are more scientific terms, thus, quicksilver 
is said to be a dense, and air a rare fluid. 

59. It is by the attraction of cohesion that liquids arrange 
themselves around a common center in globular forms ; thus dew, 
which is moisture existing in the atmosphere in very minute parti- 
cles, may be seen in the morning suspended in drops from the 
leaves of plants, and adhering to the blades of grass. Drops of 
water thrown upon an oiled surface, the globular form assumed 
by liquid mercury, hail-stones, &c, are illustrations of this power. 
On a large scale, the sun and planets may be referred to, and 
their globular form affords a strong argument to prove that they 
were originally in such a state of fluidity as allowed their particles 
to arrange themselves according to the laws of cohesion in 
liquids. 

Capillary Attraction. 

GO. Capillary* attraction is that power by which liquids rise 
through minute tubes. This is probably only a form of cohesive 

* The term capillary, is from the Latin capillus, a hair. 



58. Cohesion in liquids, 

59. Globular form of liquids. Examples. 

60. What is capillary attraction ? 



24 



NATURAL PHILOSOPHY. 



Fig. 2. 




attraction. The fluid appears to creep along as if 
attracted by the contiguous particles of the tube. 

61. The figure represents a glass partly filled with 
water, and having a small tube placed within it ; the 
fluid in the latter is seen at A, above the level at B. 
It is also seen that the fluid at B is concave, or higher 
at the sides than in the center ; this is in consequence 
of the attraction of the particles of matter which com- 
pose the ring of the glass contiguous to the upper sur- 
face of the fluid. 

62. The larger the bore of the tube, the less is 
the attractive power. If two tubes of different di- 
ameter be immersed in a vessel of colored water, it 
will be found that the liquid will rise as much higher 
in the smaller tube, B, as the diameter of its bore is 
less than that of the larger tube, C. 

63. The power of capillary attraction is manifested 
in a variety of common occurrences. If one end of a 
piece of bread be dipped in water, the liquid will soon 
make its way until the whole is moistened. The 

wicks of candles and lamps supply the flame by means of tallow 
or oil, which ascends through the capillary tubes of the cotton. 
Rocks are sometimes split by driving into a crevice a wedge of 
dry wood, which, being exposed to rains, swells by the absorption 
of water, with sufficient force to rend asunder the hardest stone. 

64. It might appear that the mercury in the small tube of a 
thermometer rises by means of capillary attraction. But this is 
not the fact, as in order that this kind of attraction should take 
place, the tube must be composed of a substance which attracts the 
particles of the liquid with greater force than they attract each 
other ; thus, particles of mercury cannot be attracted by those of 
glass ; while mercury rises in small tubes of tin or silver, and also 
in glass tubes coated with oil. 

65. Capillary attraction is only another form of cohesion, which, 
in modern science is included under the general term, molecular 
attraction, the attraction of molecules, atoms or minute particles. 

66. Chemical attraction or affinity, is that force which unites 
dissimilar particles, and cannot, like cohesion, be overcome by any 
mechanical force, such as pounding, grinding, &c. 



61. 1st experiment. 

62. 2nd experiment. 

63. Familiar examples of capillary attraction. 

64. Does capillary attraction affect the mercury in the tube of the ther- 
mometer? 

65. Molecular attraction. 

66. Chemical attraction. 



GRAVITY. 25 

67. Magnetic attraction is the power possessed by the load- 
stone or magnetic iron, of drawing towards it portions of iron or 
si eel. This power causes the magnetic needle to point directly 
towards the poles of the earth. 

68. Electrical attraction is a property which certain bodies 
possess, when excited by friction, of attracting other bodies. 



LECTURE IV. 



GRAVITY. 

69. Ml terrestial bodies fall toward the earth when not sup- 
ported. Before the 17th century, mankind had never thought of 
inquiring why bodies thus fell. It is related that the fall of an 
apple from a tree, under which the young Sir Isaac Newton was 
sitting, was the occasion which led him to philosophize on the 
subject of falling bodies. " Why," he reasoned, " did this apple 
take a downward, rather than an upward direction, or why did it 
move at all ? There can be no motion without force ; the tree 
did not push the apple down ; where then is the force which 
caused its descent ?" In considering the subject farther, he re- 
flected that the earth, everywhere, attracted bodies towards its 
surface, in the deep valleys and upon the high mountains. This 
power of attraction he called gravitation. 

70. It was something to have been the first to reflect and reason 
upon the cause of a fact, which had escaped the inquiry of all 
preceding philosophers. But Newton stopped not here ; — he be- 
held the moon pursuing her regular course around the earth, and 
was led to inquire whether she was attracted towards the earth ; 
and if so, why she too did not fall upon its surface. The result 
of his reasoning was the discovery that gravitation is not con- 
fined to the earth, but that its power pervades the solar system, 
causing not only the motion of the moon around the earth, but 
the revolutions of the earth and other planets around the sun. 
There are reasons also for believing that the same principle of 
gravitation operates in the most distant regions of space, binding 

67. Magnetic attraction. 

68. Electrical attraction. 

69. Discovery of gravitation. 

70. Its extent. 



26 NATURAL PHILOSOPHY. 

together other solar systems, and perhaps causing them and our 
own system to revolve around some common center. 

71. The attraction of gravitation or gravity is that force by 
which distant bodies tend towards each other. It diners from co- 
hesion and chemical attraction in not requiring the particles of 
matter to be brought in contact, but acts on remote bodies like 
electricity and magnetism. The cause of gravitation is not known. 
Some have imagined that a subtle, invisible fluid, issues from 
bodies which is constantly tending to draw them together. But 
the student has nothing to do with speculations unsupported by 
observation, and experience ; his object is to learn the pheno- 
mena* of gravitation, for these the Almighty has given his crea- 
tures power to understand. 

72. Our views will now be directed to terrestrial gravity. All 
bodies tend toward the center of the earth by the attraction of 
gravitation. This is not owing to any peculiar power of attraction 
in the center; but the earth being a globe, each of its own parti- 
cles is attracted to that point which thus becomes the center of 
attraction to other bodies. The terms upward and downward 
have relation to what is farthest from, or nearest to the surface 
of the earth, every part of which is equally distant from the cen- 
ter ; the slight inequality of mountains and valleys, being, in com- 
parison with the whole circumference, of 

Fig. 4. no perceptible importance. 

Let the figure represent the globe of the earth, 
and suppose bodies could fall freely from any 
point on its surface through its diameter ; a ball 
dropped from either of the points, A, B, C, &c. 
would be attracted towards at the center, and 
move in a straight line to that point where it 
would rest. The lines a A, b B, &c. are all 
vertical, and point downward, or to the center. 
Thus, we perceive that all bodies will fall per- 
pendicularly to the surface of the earth, and, if 
not impeded, would penetrate to the center 
atO. 

* Phenomenon in common language signifies some extraordinary appear- 
ance ; in science it means merely a change of appearance. Phenomena is 
the plural of phenomenon. 

71. Definition of gravity. Cause of gravitation unknown. 

72. Terrestrial gravity. Why are bodies attracted to the center of the 
earth ? To what do the terms upward and downward relate ? 




GRAVITY. 



27 



Fig. 5. 



7 



1] 



73. The real figure of the earth was not un- 
derstood by the ancients. They supposed it to 
be a flat mass of matter, whose surface only was 
habitable, and that A B were the extreme im- 
passable points. When the opinion was first ad- 
vanced that the earth was a sphere, and that there 
were inhabitants on the opposite side of its sur- 
face, it was considered as a heresy, and treated 
with great severity, both by civil and ecclesiastical 
rulers. " If there are people," said they, " who 
live on the other side of the globe, they must have their heads downwards 
and their feet upwards; and how could they hold fast to the under side of 
this ball? It is an insult to religion and common sense to pretend such a 
thing." Some attempted to explain the matter by asserting that the anti- 
podes* he'd to the surface of the earth, as iusects 
crawl on the under, as well as the upper side of a 
small globe. But they did not reflect that the in- 
sect adheres thus by means of its claws. Naviga- 
tors, in sailing around the globe, have neither 
found people with claws, nor any who considered 
themselves as living on the under side of the globe; 
all, alike, have the broad arch of the heavens above, 
and the firm earth beneath them. Besides, let us 
recollect that in twelve hours, by the earth's rota- 
tion on its axis, we shall be where our antipodes 
now are. The figure represents the sphere of tho 
earth, with two figures standing at opposite points. 
Were each at the same moment to drop an apple, 
the two apples would fall towards the earth, and 
supposing they were able to pass freely through it, 
would penetrate to the center, and being attracted 
equally, on all sides, would there remain at rest. 

74. Weight is the force with which a body is attracted to the 
earth, and this force is in proportion to the quantity of matter. 
The quantity of matter does not depend on the size of the body. 
A. piece of lead weighs heavier than a block of wood of the same 
size, because the lead has more density than the wood, or, within 
the same bulk, it contains more particles of matter. 

75. As the force of the earth's attraction is in proportion to the 
quantity of matter, if this quantity were doubled, bodies near its 
surface would weigh twice as much as they now do ; or if the 
earth contained only half its present quantity of matter, the weight 
of bodies would be lessened in the same proportion. 

* Antipodes is from the Greek anli against, podes feet. 




73. Opinion of the ancients respecting the figure of the earth. 

74. What is weight ? Does the quantity of matter in a body depend on 
its size ? 

75. In what case would bodies weigh twice as much as they now do ? 



28 



NATURAL PHILOSOPHY. 




Fig. 8. 




76. V/eight is measured by its mechanical ef- 
fects, such as bending a spring, or turning a bal- 
ance ; or, it is measured by the force that it takes 
to hold a body back to keep it from falling. 

77. The balance consists of a horizontal bar, so suspended 
that its two arms, with the scales attached, are in exact 
equilibrium. A merchant wishing to weigh a pound of* tea, 
puts into the scale a, a leaden pound weight, which by its 
gravity, causes the scale to descend. As the article to be 
weighed, is put into the other scale b, a begins to rise, and 
when the mass equals that of the leaden pound weight, 
the two scales are again in equilibrium, as at Fig. 8. 

78. The bulk of a pound of tea is greater than 
that of the leaden pound weight ; hence, we say, 
the specific gravity of the latter, is greater than 
that of the former. 

79. We have said that all terrestrial bodies are attracted toward 
the earth. It may be objected that this is not the fact with respect to 
smoke, steam, and especially the gas* used to innate balloons, which 
not only raises the balloon, but carries the aeronaut into the higher 
regions of the atmosphere. But these and similar phenomena 
are, in reality, instances of the effects of gravitation, for the as- 
cending bodies are driven upward solely by the force of the me- 
dium through which they pass ; since the particles of smoke or 
vapor, or the balloon, cannot advance upward without displacing 
portions of the atmosphere equal to their own bulk. A block of 
wood when plunged into a vessel of water rises and floats upon 
the surface, because the specific gravity of wood is less than that 
of water, and the heaviest body being most strongly attracted 
forces the lighter one upward. Lead, on being thrown into a ves- 
sel containing mercury, will swim on the surface, and, if forced 
down, it re-ascends ; but gold in the same situation, will sink. The 
specific gravity of gold is greater, and that of lead less than that 
of mercury. 

80. Air being lighter than the solid and liquid bodies on the 
earth keeps its place above them ; but air has weight, being sub- 
jected to the universal law of gravitation. The air near the sur- 
face of the earth is more dense than in the upper regions. Per- 
sons who ascend high mountains or rise to great heights in bal- 
loons find a difficulty in breathing on account of the rarity of the 
air. The increased density in the lower strata of the atmosphere, 

* Hydrogen. 



76. How is weight measured ? 

77. The balance. 

78. Specific gravity. 

79. Why do smoke, steam, &c. ascend ? Wood and lead made to swim, 

80. Has air weight ? Unequal density of the air — its cause. . 



GRAVITY. 29 

is owing to the pressure of the upper portions ; as the lower 
fleeces in a pile of wool are more compact, or dense, than those 
which are not subjected to the same degree of pressure. 

81. Pressure, as well as the motion of falling bodies, proves 
that attraction is universal. When a stone is held in the hand, the 
pressure is in proportion to its quantity of matter. It is eAddent that 
a force is in operation tending to draw the stone downwards. 

8*2. As the force of gravitation is proportioned to the quantity 
of matter, it follows that all bodies would fall with equal velocity, 
if they met with no resistance. A feather and a leaden bullet, 
dropped from a given height together, would reach the ground at 
the same instant, were it not for the resistance of the air, which 
the lighter body cannot so readily overcome. The medium through 
which bodies fall, impedes their descent, in an inverse* proportion 
to the specific gravity of these bodies. By means of an appara- 
tus called an air-pump, we are able to exhaust, or pump out the air 
from vessels placed over it. 

83. The attraction of gravitation is reciprocal ; that is, every 
particle of matter attracts every other, as much as it is attracted by 
it. If the larger of two bodies have four times the number of par- 
ticles as the smaller, it would exert four times as much attractive 
force ; or, cause the smaller body to move with four times as great 
velocity as it would, if the masses of the bodies were equal. It is 
owing to the immense difference between the mass of the earth and 
that of any one body on its surface, that the attractive influence of 
bodies falling towards the earth, produces an effect too slight for 
observation. The earth, though held in its annual motion by the 
attraction of the sun, a body one million of times greater than itself, 
has no perceptible effect on the sun's position. The Moon is made to 
revolve round the earth, its superior in size ; yet the attraction of 
the moon is sensibly felt upon the earth, in the production of tides. 

84. The resistance of the air is always in proportion to the 
surface of bodies ; a lump of gold that would, in falling, seem 
little impeded by this resistance, may be hammered into thin sheets 
called gold leaf so that the same particles of matter shall cover 
a surface many millions of times greater; and the increased resis- 
tance of the air will be in proportion to the increase of surface. 

* By inverse is meant contrary to, or the opposite of, from the Latin in, 
and verto, to turn. 

81. Pressure. 

82. Do all bodies fall with equal velocity? Why would not a feather fall 
to the ground from any given height, in the same time that a bullet would 
fall from the same height? 

83. Attraction of gravitation reciprocal. 

84. Resistance of the air, in proportion to what ? 

3* 



30 



NATURAL PHILOSOPHY. 



Fig. 9. 




85. Bodies in falling, unless drawn aside by some other force, 
always move in lines perpendicular to the surface of the earth. If 
a small piece of lead be suspended by a cord, the 
latter will hang in a vertical line. This is called 
a plumb or plummet line (from the Latin, plumbum, 
lead ;) it is of great use to mechanics in finding the 
true perpendicular, for the walls of buildings, <Scc. 
The floors of a house should be in a horizontal 
plane or level, the walls and partitions perpendic- 
ular. 

86. A plummet line suspended from a high 
mountain, is drawn from the perpendicular toward 
the side of the mountain ; this is owing to the at- 
traction of the mountain, which, though small in 
comparison to the whole earth, is capable of inter- 
fering with its attraction, because gravity diminishes 
as the squares of the distance increase ; in this case, 
the attraction of the smaller body, on 
account of its nearness, overcomes 
that of the larger, but more distant 
body. 

87. No two bodies can fall to the 
earth in parallel lines, for as they are 
all attracted to the center, the lines, if 
prolonged, must continue to approach, 
until they meet in that point. 

Thus, the two sides of a pair of scales do 
not hang exactly parallel to each other ; A 
B C represents the earth's sphere, and E 
D a balance suspended over it. The lines 
D F and E F, which meet in the centre of 
the sphere, are hot parallel, for parallel 
lines, if produced to any length, never meet. 
The convergence* in common scales is 
too slight to be perceptible to our senses ; 
but in the figure, the beam of the scales is 
represented as extending through several 
degrees of the earth's circle. 

88. WJiere there is no attraction 
there can be no weight. If there 

* Converging lines are such as incline toward each other, and if suffi- 
ciently extended would at length meet. 




85. Plumb-line. 

86. Why will a plummet-line suspended from a high mountain be drawn 
from the perpendicular ? 

87. Can two bodies fall to the earth in parallel lines ? 



GRAVITY. 31 

were but. one body in the universe, it is evident that this would 
be attracted by nothing, and remain at rest ; and, though it were 
of the magnitude of the sun, together with that of all the planets, 
it would not press in any direction sufficiently to counterbalance 
the weight of a feather. 

89. T lie force of gravity is greatest at the surface of the earth, 
from whence it decreases both upward and downward. In ascend- 
ing from the earth's surface, the force of gravity decreases as the 
squares of the distance from the center increase. This proposi- 
tion asserts, that as the distance from the center of the earth in- 
creases, the force of gravity diminishes ; and that the degree of 
diminution is not simply proportional to the increase of distance, 
so as to be one-half at double the distance, and one-third at three 
times the distance, but it is proportioned to the square of the dis- 
tance, so that at twice the distance it is only one-fourth as great, 
at three times the distance only one-ninth, &c. 

90. The square of any number is that number multiplied by 
itself; thus the square of 2 is 4, the square of 4 is 16, the square 
of 16 is 256, &c. A body, which at the surface of the earth, viz. 
4000 miles from the center* would weigh one pound, if carried to 
twice this height from the center, namely, 8000 miles, would 
weigh one-fourth of a pound; if carried 12000 miles from the cen- 
ter, or three times the distance of the surface of the earth from the 
center, its weight would be diminished to one-ninth of a pound. 
The moon is about sixty times as far from the center of the earth 
as the distance from that center to the surface, (that is, 240,000 
miles); therefore, as the square of 60 is 3600, the attraction of the 
earth at the moon is 3600 times less than at the earth's surface ; 
so that a body which here weighs one pound, would, at the dis- 
tance of the moon, weigh only the three thousand and six hun- 
dredth part of a pound. 

91. The force of gravity from the earth 's surface downwards, 
decreases simply as the distance ; so that at 2000 miles, or half 
way from the surface to the center, a body weighing one pound at 
the surface would weigh but half a pound ; at 3000 miles, or three- 
fourths the distance from the surface to the center, it would weigh but 
one quarter of a pound ; and at the center it would have no weight. 

* Or half the diameter of the earth. 

89. Where is the force of gravity greatest? State the law of gravity at 
different distances above the earth's surface. 

90. What is meant by the square of any number? By what method of 
calculation can we determine what would be the weight of any body at the 
moon, its weight at the earth's surface being ascertained ? 

91. How does the force of gravity from the earth's surface downwards 
decrease ? 



32 



NATURAL PHILOSOPHY. 



92. A body situated within a hollow sphere would remain at rest tn any 
part of the void. Suppose the earth to be a hol- 
low sphere, surounded by a crust A. C. ; a ball, B, 
introduced into the empty space would remain at 
rest; for while the nearer portions of the crust, on 
the right of the line A C, would attract the ball 
more than the remoter portions, on the left of the 
line A C, the greater quantity of matter on the 
latter side would be an exact counterpoise. 

93. A body carried from Philadelphia 
to the north pole would gain in weight ; if 
carried to the equator it would lose in 
weight. This is owing to the spheroidal 
form of the earth, or its being flattened at 
the poles, which are somewhat nearer the 
center of the earth than is the equator ; the poles being nearer 
the center of attraction, the force of gravity is greater there than 
at the equator. 




LECTURE V. 



CENTER OF GRAVITY. 



94. The center of gravity is that point in a body, about which, 
the body acted upon only by gravity, will balance itself. There- 
fore, if a body be supported by the center of gravity, it will rest 
in any position, and, whatever supports that point bears the weight 
of the whole mass. A cane may be poised upon the finger, its 
center of gravity being supported. 

95. Though in any mass of matter, every atom has its separate 
gravity and inertia, and the weight and inertia are, in reality, dif- 
fused through the whole, yet, as there is one point which, when 
supported, balances the whole, and, when not supported leaves 
the whole to fall, the weight of the body may be considered as 
centered at that point. 

96. In a body of a regular figure, and composed of a substance 
of uniform density, the centime of gravity is the same as the center 



92. Suppose a body situated in a hollow sphere. 

93. Difference in the weight of bodies at the equator and the poles. 

94. What is the center of gravity ? 

95. What is the center of weight ? 

96. Is the center of magnitude always at the same point as the center of 
gravity ? 



CENTER OF GRAVITY. 



33 



of magnitude, as in a cube of wood, or ball of lead; this center 
of the cube or ball is also the center of gravity. 

In the following figures, the lines intersect each other in the center of the 
figure, and supposing each to be of a uniform density, this center is also the 
point around which the quantities of matter are equal on all sides, and 
therefore exactly balance each other. 

Fisr. 12. 





- 


/-:/ 








97. If a body be suspended from a fixed point, the center of 
gravity will always be in a vertical line beneath the point of sus- 
pension. 

In the case of a body of equal thickness but of an irregular form, as a piece 
of board, to find the center of gravity, suspend it by one corner, and from 
the same corner let fall a plumb-line, and mark its direction on the board. 
Now suspend the board from any other point, marking the direction of the 
plumb-line as before, the point of intersection of the two lines is the center 
of gravity. 

98. A vertical line drawn through the center of gravity, is 
called the line of direction. If the line of direction fall within 
the base of the body, it will stand ; but if it fall without the base, 
the body will fall. 

99. A carriage moves securely over a level road, because the 
center of gravity falls between the wheels, - and is supported. 

Where one side of the road is much higher 
than the other, there is always danger that 
a carriage will be overturned ; and this dan- 
ger is increased, in proportion as the height 
of the carriage or of the load is increased. 

Suppose A to be the center of gravity, the line of 
direction (or the line which is drawn through the 
center of gravity perpendicular to the earth) is then 
towards C, which, not falling within the wheels, is 
not supported by them, of course the load must 
be upset. But supposing part of the load to be 
taken off, or that instead of some light loading, such 
as wool or hay, the cart were loaded with iron or 
stone, the center of gravity would then be lower, 
as at B, and the line of direction, B D, being thus 
within the wheels, the body would be supported. 



Fig. 13. 




97. How is the center of gravity found ? 

98. What is meant by the line of direction ? 

99. Why does a carriage move most securely over a level road 1 Effect 
of height in increasing the danger of upsetting a load. 



34 



NATURAL PHILOSOPHY. 



100. The form of bodies is of great importance in giving them 
firmness of support ; for, while some cannot be moved without lift- 
ing the center of gravity, others can be set in motion by the slight- 
est force. The broader the base, and the nearer the line of direc- 
tion to the center of it, the more firmly does a body stand ; while, 
the narrower the base of a body, and the nearer the line of direc- 
tion to the side of it, the more easily it is overthrown. 

101. In the following figures, the two particulars, base and height, are 
combined in a series of proportions. The place of the center of gravity in 




Fig. 15. 



each figure is marked by a dot, and the curved line proceeding from it shows 
its path when the body is overturned. This curved line is a portion of a 
circle which has the edge or extremity of the base b, in Fig. A, as a center, 
because the body in turning, must rest upon such extremity, or corner as the 
center of its motion: n shows the line of direction, or where a plummet line, 
if suspended from the center of gravity, would fall. In Fig. A, the base is 
broad, and the center of gravity is low ; before the body can fall, this 
center must l-ise almost perpendicularly ; and the resistance in overturning 
it, is, therefore, nearly equal to the weight of the whole body. Figures B, 
C, and D, show the lines in which the body must fall, to be more and more 
inclined as their bases become narrower; 
consequently the bodies stand less firmly in 
proportion. B represents a square house; C 
a tall, narrow house ; and D a very high chim- 
ney. At Fig. E, the center of gravity being 
over a base which is a mere point, the body 
is in a tottering position, and at the least de- 
gree of inclination would fall. When a round 
body is rolled on a horizontal plane, the cen- 
ter of gravity is not raised, but moves in a 
straight line parallel to the surface of the plane 
on which it rolls ; the center of gravity, there- 
fore, is always directly over the center of mo- 
tion. B is the plane on which the ball moves, 
A the line in which the center of gravity moves, and C a plumb-line ; D is 
the center of gi-avity, directly above the center of motion. A ball on a hori- 
zontal plane will rest with equal firmness in any position, and the center of 
gravity will describe a horizontal line over that of motion, in whatever direc- 
tion the body is moved. If the plane is inclined downward, the ball will be 




100. Importance of the form of bodies in giving them firmness, 
gravitation in respect to the form of bodies. 

101 Various forms of bodies in relation to base and height. 



Law of 



CENTER OF GRAVITY. 



35 




set in motion, the center of gravity being in advance of the centre of motion, 
or that point on which the bull rested. 

102. Spherical bodies are easily 
rolled down an inclined plane, because 
their base is but a point, and the small- 
est force is sufficient to remove the 
line of direction out of its base. We 
_ perceive by the lines of direction, F 
H K, that the body A will slide down 
the plane D E, while B and C will roll down the same. 

108. A ball or cylinder rolls downwards by the force of gravi- 
tation, because its center of gravity in approaching the earth, is 
continually urging forward the center of motion. The difficulty 
of rolling heavy bodies up an ascent, arises from the fact that the 
center of gravity is behind that of motion, and continually tending 
to impede its progress. 

104. The center of gravity in any body which is left free to 
assume its natural position, is such, that a line drawn from this 
center to the point where the body rests, will 
be the shortest that can be drawn from the 
center to any part of its surface. Thus an 
oval body would not stand in the position* re- 
presented in the figure, but would turn until 
the shorter line, A C, became perpendicular to 
the supporting surface instead of the longer line, 
A B. The center of gravity, when bodies are not 
supported, always seeks the lowest situation. 

105. In the case of an irregular solid, 
let us suppose the figure to represent a 
piece of board suspended from the point a ; 
let a plumb line, a g, also be suspended 
from a, and mark the direction of the string 
on the surface of the board. Then sus- 
pend the board from any other point, as d y 
and also the plumb line from the same 
point, and mark its direction ; the point c, 
where the two lines cross each other, is 
the center of gravity. 
106. A ball or cylinder may be made to roll up an inclined 
plane by its own weight. Let A B, represent a cylinder of light 



Fig. 17. 




102. Why are spherical bodies easily moved? 

103. Why is it difficult to roll heavy bodies up an ascent ? 

104. When bodies are left free, where will the center of gravity rest ? 

105. How can the center of gravity be found in an irregular solid ? 

106. How can a cylinder be made to roll up an inclined plane ? 



NATURAL PHILOSOPHY. 



Fig. 19, 



wood, having its center of gravity at 
c, and placed on the inclined plane C 
D ; it is evident, that as its line of di- 
rection from the center of gravity lies 
out of its base, it would roll down ; but 
if at e, a ball of lead be inserted into 
the cylinder, it will then roll upwards 
till the lead gets as near the surface of the plane as possible, and 
therefore when the cylinder is ascending, the lead is descending. 




Fig. 20. 




Fig. 21. 



107. Another experiment of a similar kind serves, also, to show the effect 

of the unequal distribution of weights in 
different parts of amoving body. A double 
cone, C, (Fig. 20) united at the base, will 
ascend the inclined plane, made by open- 
ing a jointed rule, A B, and raising it at 
the open end, A D. But though the cone 
ascends, its center, which is the center 
of gravity, really sinks lower and lower 
between the sides of the rule, as it ad- 
vances to the open end. 

108. The figure of a horse, with only 
the hind feet supported on a pedestal, 
represents a toy in which the weight of 
a ball below the horse, by bringing down 
the center of gravity, causes a vibratory 
motion when either the rider or horse is 
touched. 

109. Let A B represent a stick resting 
on the edge of a table; if left to itself 

this would fall, bacanse its center of 
gravity is beyond the table ; but the 
pail, C, being suspended by a string, 
s, from the stick, A B, instead of 
pulling it down, supports it by 

107. Ex. of the double cone. 

108. Scientific toy. 

109. How can a pail of water be 
supported by a stick lying loosely on a 
table. 




C'ENTEK OF GRAVITY. 



37 



Fig. 23. 




means of another stick, C B, which rests against a niche in the end of A B 
and presses against the string at the point from which the pail is suspended. 
Now the stick, A B, cannot fall without lifting the weight of the pail, or 
raising the center of gravity. On the opposite side of the table at F, is a 
common tobacco pipe, which may be made to sustain any weight that is not 
sufficient to destroy the cohesion of its particles. 
An umbrella or walking cane, hanging on the 
edge of a table is supported on a like prin- 
ciple. 

110. A building, though leaning consider- 
ably from the perpendicular, will not fall, so 
long as the center of gravity is supported. 
A column or steeple might, without en- 
dangering its stability, have an inclination 
as great as that in the figure, where A B re- 
presents the line of direction ; but this would 
not be the case, where C D falls without 
the base. 
111. Tall spires and turrets, after a lapse of time, are often 
seen to lean from the perpendicular ; but if 
they are properly constructed, they may long 
endure, even in this state. In Pisa in Italy, 
where are many ancient and remarkable 
buildings, is a celebrated leaning tower, 
which was built in the twelfth century. It 
is of marble, 168 feet in height, and leans 
sixteen feet from the perpendicular. Some 
suppose, that this beautiful tower was de- 
signedly built in this manner, to excite emo- 
tions of wonder in the spectator, be- 
holding its lofty top thus bending over its 
base. Others believe it to have gradually 
sunk to its present position. An illustration 
of the leaning tower may be made by piling 
blocks of wood upon each other, as repre- 
sented in the figure. When the third block 
is added, the centre of gravity is within the 
base, as shown by the line of direction A, 
and the column, though leaning, is support- 
ed. But when the fourth block is added, the 
"~=^= line of direction B, being without the base, 
the column falls. 




B A 



112. When two bodies of equal weight are connected by a 
rod, the center of gravity will be in the middle of the rod, and a 



110. Building leaning from the perpendicular. 

111. Tower of Pisa. How illustrated. 

112. Center of gravity in two bodies connected. 




© 



38 NATURAL PHILOSOPHY. 

string fastened to this point 
Fig. 26. will hold the whole in equili- 

brium. But, if the bodies are 
of unequal weight, the center 
£ of gravity is nearest the great- 
er weight. That is, if a be a 
weight of three pounds, and b 
a weight of one pound, a string 
fastened to the point c, three times nearer to the center of the 
large weight, than to that of the small one, will hold the two 
bodies in equilibrium. 

113. A person can carry two pails of water, at the same time, 
with nearly as much ease as he could carry one, because the two 
pails balance each other, and the feet more naturally sustain the 
center of gravity than when this is thrown on one side by the 
weight of a single pail. 

114. The center of gravity is also the center of inertia. 

115. If a person lift a rod of uniform density by the middle, he 
overcomes the inertia of the whole mass. If he lift it by a part 
nearer to one end, the shorter, and consequently the lighter part, 
will rise first, because the center of inertia is in the other. 

116. We perceive the intimate connection between the principles of Natu- 
ral Philosophy and the mechanic arts, since not even a chimney can be con- 
structed without constant reference to the plumb line. The moderns, in 
their structures, study elegance and comfort rather than durability ; the 
walls of modern brick and stone buildings, being so slight, that if they vary, 
in the least, from the perpendicular, they are in danger of falling. They af- 
ford in this respect, a great contrast to the massy piles of antiquity. 

117. Force applied to the center of inertia or gravity, will pro- 
duce an effect which cannot be produced by much greater force, 
acting on other portions of a body. A blow with a hammer upon 
a large rocking stone, if falling upon a part distant from the center 
of inertia, (or gravity,) might destroy the cohesion of particles, so 
as to break off a portion of the rock without moving the whole 
mass ; while the same force, so applied as to affect the center of 
inertia, would set the rock in motion. If the motion were to begin 
on a horizontal plane, it might stop with overturning the rock ; 
but if, on the downward side of a hill, the rock would continue to 
move to the foot of the declivity, and as much further on the level 
ground, as the impulse received from the original blow and from 

113. A person carrying two pails of water. 

114. Center of Inertia. 

115. Inertia overcome. 

116. Mechanic arts connected with Philosophy. 

117. To what point in a body should efforts to remove a leavy body be 
applied ? In what case might a portion of a rock be broken off, without 
moving the whole mass ? 



CENTER OF GRAVITY. 39 

velocity would carry it. The resistance of friction would at length 
overcome the inertia of motion. 

118. The motions of animals, of man in particular, illustrate 
the foregoing laws icith respect to the center of gravity. We 
have found, that a body with a narrow base is less easily sup- 
ported than one with a broad base, and that the greater height 
requires the greater base ; but man walks erect, firmly supporting 
his tall figure on a very narrow base, and in a variety of atti- 
tudes. This supporting base is the space occupied by, and in- 
cluded between the feet. 

Persons who turn the toes outward in walking, have then the ad- 
vantage of a broader base, which adds, not only grace, but firmness to their 
gait. We may, in varioifs attitudes of human beings, perceive these two 
qualities, grace aud firmness, intimately connected ; by this we mean, that 
those positions in which the center of gravity is best supported, are the 
most graceful. The best rule for fine attitudes is, to keep the center of 
gravity of the body well over the base. This center in the human being is 
between the hips; by setting the feet in parallel lines, and close together, 
the figure is not firmly supported, and considerable muscular effort is ne- 
cessary to keep the body erect. 

119. In sitting down, or in rising from a seat, much of the grace of motion 
depends on the manner in which the center of gravity is lowered or raised. 
Some persons drop into a chair as if they were lumps of inert matter, influ- 
enced only by gravitation ; whereas the muscles of the lower limbs should 
be so exercised that the center of gravity may descend slowly, and gracefully. 
In rising from a seat, the body must be inclined forward, to bring the center 
of gravity over the feet or base ; and, in this position, the muscular force of 
the hips and lower limbs is sufficient to effect the object. 

120. It is said that a man having agreed to give ten guineas for the privi- 
lege of attempting to possess himself of a purse of twenty guineas, by pick- 
ing it up when laid before him on the floor, lost his money. The conditions 
were that he should stand with his heels against a perpendicular wall, and 
in this position, should pick np the purse. Under these circumstances, the 
forward inclination of the head and arms would throw the center of gravity 
beyond the base, and the man must fall ; in order to reach the floor with his 
hands, it was necessary to throw one foot backward, which the wall pre- 
vented. 

121. In walking, the center of gravity is alternately over the right and 
the left foot ; if one foot be injm-ed so that it sustains the weight of the body 
with difficulty, the lame person advances only with the well foot, using the 
other merely to rest upon, while the well foot moves the weight. A man 
carrying a burden on his back, leans forward ; if the weight be in his arms, 
he leans backward ; if on his head, he walks erect. If the load be on one 
shoulder, he leans to the other side. When a man stumbles with one foot, 
he extends the opposite arm. In ascending a hill, he bends forward, and in 
descending he leans backward. In all these cases the object is, to support 
the center of gravity, and to bring the center of direction within the base, 
that is, the feet. 

118. Laws of gravity illustrated by the motions of animals. 

119. Rising up, and sitting down. 

120. Why could not a man pick up a purse, and at the same time stand 
with his heels against a wall ? 

121. Change of the centre of gravity in walking, &c. 



40 NATURAL PHILOSOPHY. 

122. The young child does not learn to stand, much less to 
walk, till long practice in position has taught him how to support 
his weight, and the muscular efforts necessary to move it. The 
kitten, and other quadrupeds, sustained by broad bases, have no 
need to learn the art of standing. But we seldom see the§e ani- 
mals raising the two feet on one side, at the same time. 

123. The vegetable kingdom, no less than the animal, is sub- 
jected to the laws of gravitation. Tall trees have their roots 
wide spreading, in proportion to their height, thus furnishing a 
broad and firm basis of support. Their line of direction, also, is as 
unerring as in any works of art ; the pine and fir grow as perpen- 
dicularly as the builder can construct a column. Who will say 
that a divine master builder does not rear these stately pillars of 
nature's temple ! Upon the hill side as upon the level plain, with 
undeviating regularity do they rise toward heaven, as if to do 
homage to their Creator. 



LECTURE VI. 

MOTION AND FORCE. LAWS OF MOTION. 

124. All bodies are either in a state of rest or motion. They 
have no tendency to the one state more than the other ; but re- 
quire force not only to put them in motion when at rest, but to 
cause them to stop when once in motion. 

125. Motion may be defined a change of place. 

126. Absolute motion is a change of place with respect to any 
fixed point ; a person walking or riding is in absolute motion. 

127. Relative motion is a change of place in a body in motion, 
with respect to another body, also in motion. Suppose a person 
standing on that part of the deck of a steamboat farthest from the 
shore, should, at the moment of the boat's starting off, begin to 
run towards the shore, and move, at the same rate at which the 
boat was moving, to the other end of the deck ; his position with 
respect to the objects on shore, would be, exactly, what it was 
when the boat started, though changed in relation to the boat, 

122. Why does a young child find it more difficult to support its weight 
than young quadrupeds ? 

123. Have the laws of gravity any influence in the vegetable kingdom. 

124. Have bodies any more tendency to a state of rest than of motion. 

125. What is motion? 

126. Absolute motion. 
327. Relative motion. 



MOTION. 41 

128. Apparent motion is caused by the real motion of the spec- 
tator. Li moving swiftly along, in a carriage or boat, the objects 
around us appear to be in motion ; those we have past, seeming 
to recede, and those before us, to approach. The motion of the 
earth on its axis, causes the apparent motion of the sun ; thus we 
say " the sun rises or the sun sets," as the passenger on board a 
vessel says " the shore is receding from us." 

129. We have remarked upon that property of matter called 
inertia, or a passiveness, with regard, either to motion or rest ; 
as there is nothing within, which can put inert matter in mo- 
tion, this effect must be produced by the agency of some exter- 
nal power ; this power is called force, 

130. Force, may be muscular, as in the action of men and animals; 
or mechanical, as in the action of wind, water, steam, and gravity. 

131. Velocity, is a term applied to bodies in motion. A bird 
darting through the air, moves with great velocity; a tortoise moves 
with little velocity ; that is, the time in which the bird and the 
tortoise would pass over a given space, would be different. 

132. The velocity of motion is estimated by the time spent in 
moving over a certain space, or, by the space moved over in a cer- 
tain time. The less the time, and the greater the space moved 
over, the greater is the velocity ; but the greater the time, and the 
less the space moved over, the less is the velocity. 

133. To ascertain the degree of velocity, divide the space by 
the time ; — suppose a person travels 30 miles in 6 hours ; to 
know his velocity, divide 30 by 6, the answer is 5. That is, he 
traveled at the rate of 5 miles an hour ; thus velocity equals 
space divided by time. 

134. To ascertain the time in which motion is performed, divide 
the space by the velocity ; — if a man has traveled 30 miles, at the 
rate of 5 miles an hour, (as 30 divided by 5 is 6,) in 6 hours, he 
has performed the journey. 

135. To ascertain the space moved over, multiply the time into 
the velocity ; — thus, 6 hours representing the time, is multiplied by 
5, which stands for the velocity, or rate of motion, and the answer 
is 30, which stands for space, or distance traveled. Where any 
two of the three circumstances, velocity, time and space are given, 
the third may be ascertained. 

128. Apparent motion. 

129. What is the power called which produces motion? 

130. What are the different kinds of force ? 

131. What is velocity? 

132. How is velocity estimated ? 

133. How can you ascertain the degree of velocity ? 

134. How can you ascertain the time in which motion is performed ? 

135. How the space moved over? 

4* 



42 NATURAL PHILOSOPHY. 

136. The rules above given, apply only to cases of uniform 
motion, that is ; when the body passes over equal spaces in equal 
portions of time, as the index of a clock. 

EXAMPLES. 

1. If a bird fly 6,000 feet in 5 hours, what is its velocity per 
ninute ? Ans. 20 feet. 

2. A carriage passes over 28 miles in 7 hours, what is its velo- 
city per hour ? Ans. 4 miles. 

3. If a boat is propelled by the oars 4 miles an hour, and by 
the current 2 miles an hour, how long will it be in passing over 
24 miles ? Ans. 4 hours. 

4. A western emigrant travels 5 miles an hour, how far will 
he go in 4 days, traveling 10 hours each day 1 Ans. 200 miles. 

137. Accelerated motion is when the space described in equal 
portions of time continually increase, as in the case of bodies fall- 
ing by the force of gravity. 

138. Retarded motion is when the spaces described in equal 
portions of time continually decrease ; the motion of a body 
thrown upward is continually retarded by the earth's attraction. 

139. The momentum of a body is its moving force, or quantity 
of motion, and this is in proportion to its weight and velocity. 

140. A cannon ball, thrown against a person with the hand, 
might have only momentum enough to bruise the flesh ; while the 
same ball shot, at the same distance, from a cannon, would pass 
through the body. The weight, in both cases is the same, but the 
difference in the velocity causes the difference in the momentum. 

141. A block of wood, floating slowly against a person's limb 
suspended from a dock, would scarcely be felt, while a loaded 
vessel, moving at the same rate, would crush it. Here the velo- 
city is the same, but the weight different. 

The boy who throws a ball, or shoots a marble, knows that its 
force, or momentum, is in proportion to its velocity ; that the same 
ball will strike twice as hard if it move twice as fast, or ten times 
as hard if it move ten times as fast. Let the word momentum be 
substituted for hard, and velocity for fast, and we have the fact 
expressed in scientific terms. 

142. The momentum of bodies is one of the most important 

136. In what cases do these rules apply ? Examples. 

137. Accelerated motion. 

138. Retarded motion. 

139. Momentum. 

140. Momentum caused by velocity. 

141. Momentum of weight. Terms substituted for momentum and ve- 
locity. 

142. How do machines derive their power ? 



MOTION AND FORCE. 



43 



principles in mechanics. 
posing matter to motion. 

Fig. 27. 




Machines derive their powers by op- 

143. Force is that cause 
which moves, or tends to 
move, a body, or to change 
its motion. If the ball a, be 
placed gently against the 
block b, the force will not 
be sufficient to move it ; but 
let the same ball be placed 
at c, and rolled down the inclined plane A B, the momentum will 
be so great as to overcome the resistance of the block. In the 
former case, b would only have to resist the weight of the ball a ; 
in the latter, it has to resist the weight, multiplied into its velocity. 
The momentum of a body is proportioned to the product of its quan- 
tity of matter, and its velocity. 

EXAMPLES. 

144. A weighs 50 pounds, and moves at the rate of 20 feet 
in a second ; B weighs 100 pounds and moves at the rate of ten 
feet in a second ; what are their momenta ?* 50 multiplied 
by 20 is 1000 ; 100 multiplied by 10 is 1000 ; therefore their 
momenta are equal, being both represented by 1000. In this ex- 
ample, we see that a smaller body moving with a greater velocity, 
has a momentum equal to that of a larger body moving with leso 
velocity. 

145. A weighs 15 pounds, and moves with a velocity of 5 feet 
in a second, and B weighs 12 pounds and moves with a velocity 
of 6 feet in a second ; what are their momenta ? the momentum 

of A, 15x5=75 
ofB, 12x6=72f 

146. The momentum of bodies may be calculated by the sim- 
ple rule of multiplication. A ball, A, weighing 2 pounds, and 
moving with a velocity of 6 miles an hour, will strike with a mo- 
mentum which may be represented by the product of 2 multiplied 
by 6, viz., 12 ; and a ball, B, weighing 6 pounds, and moving 
with the velocity of 8 miles an hour, has a momentum equal to 

* Momenta is the plural of momentum. 

t X is the sign of multiplication, = of equality, thus: 12X6=72, signi- 
fies that 12, multiplied by 6, equals 72. 

143. Definition of force. To what is the momentum of a body propor- 
tioned 'I 

144. Example of equal momenta and unequal weight. 

145. Example 2nd. of equal momenta and unequal weight. 

146. Rules for calculating momentum. Examples. 



44 NATURAL PHILOSOPHY. 

these two numbers multiplied together, viz. 48. In comparing 
the momenta of the two balls, we have only to divide the greater 
by the smaller number ; thus 48 divided by 12 gives 4, so that the 
momentum of B is four times that of A, or, in other words, B moves 
with four times the force of A. 

Suppose a mass of snow weighing 2700 pounds, descends the 
Green Mountains, with a velocity of 15 feet per second ; with 
what momentum will it fall. Ans. 40,500 pounds. 

If a ball of 20 pounds' weight, fall with a velocity of 5 feet per 
second, and one of 25 pounds' weight, with a velocity of 4 feet 
per second, what are their comparative momenta 1 Ans. Equal ; 
for 20x5=100, 
25X4=100, 

147. When two bodies of equal weight meet, the shock is the 
same whether the motion be shared between them, or be wholly 
in one : — but where their weight is different, the shock is greater 
to the smaller body. If one person run against another, who is 
standing, both receive a shock. If both be running at the same 
rate in opposite directions, the shock is doubled. In some cases, 
as in swift skating, when the velocity is very great, the momen- 
tum has been sufficient to destroy the lives of those who have 
thus met. 

" When two ships meet at sea, although each may he sailing at a 
moderate rate, the destruction is often as complete to both, as if, with 
double velocity, they had struck on a rock. Many melancholy instances 
of this kind are on recoixl. In the darkness of night, a large ship has 
met one smaller and weaker, and in the lapse of a few seconds, have fol- 
lowed the shock of the encounter, the scream of the surprised victims, and 
the horrible silence when the waves had closed over them and their vessel 
forever."* 

OP THE LAWS OF MOTION. 

148. There are three important principles, or laws of motion, 
which are of extensive application in mechanical philosophy. 

First law of motion : a body continues always in a state of 
rest, or of uniform motion in a right line, till compelled to change 
that state by some external force. 

149. This law of motion is the necessary result of the inertia 
of matter, which resists any change of state, whether of motion 
or rest. The resistance of the air, friction, and gravitation, are 
forces which tend to stop motion. On account of the various ob- 
stacles which exist at the surface of the earth, we see here no in- 
stances of perpetual motion ; but the heavenly bodies in their con- 

* Arnott's Elements of Physics. 

147. Double shock caused by the meeting of bodies. 

148. First law of motion. 

149. What does the first law of motion result from ? Perpetual motion 
of the heavenly bodies. 



OF THE LAWS OF MOTION. 45 

tinued and undeviating revolutions, show the tendency of matter 
to continue in motion, when meeting with no impediments. 

150. It requires more force to produce motion in a body at 
rest, than to keep the same body in motion ; as a horse may be 
obliged to use strong efforts to start a load, which he can draw 
easily, after the resistance of rest has been overcome. In large 
bodies, motion should be applied gradually, or it may affect only 
a part of the mass, arid thus destroy its cohesion. If a team with 
a heavy load be suddenly started forward, there is danger of 
breaking the harness. The child soon learns, that when he has 
a load upon his little cart, he must pull with a gentle and steady 
force, or his string will be in danger of breaking. 

151. The effect of inertia in bodies in motion, is no less stri- 
king than with respect to those at rest. If a ship sailing with 
only a moderate velocity, suddenly stop, the passengers within, 
to whom the motion had not been perceptible, experience a 
shock, and the movable furniture is thrown forward. Should 
the earth be suddenly stopped in its diurnal motion, everything on 
its surface would be thrown eastward, or in the direction towards 
which the earth was revolving. 

152. Second law of motion: the motion of a body is in the 
direction of the force which produces it, and is proportional to 
that force. 

153. That motion is in the direction of the force impressed, is 
understood by the boy who throws a stone upwards, to bring down 
an apple* from a tree ; or who strikes his ball with the wish of 
driving it to any particular point. Another boy turns the same 
ball out of its intended course, by giving it with a side-blow an 
oblique direction. A wind blowing to one point of the compass, 
impels bodies in the same direction. The sportsman levels his 
gun, and the shot impelled by the expansive force of the gunpow- 
der, moves exactly in the direction he intends. 

154. Wlolion is proportional to the force which produces it. To 
throw a ball weighing two pounds, a distance often feet, requires 
twice as much force, as to throw a ball weighing one pound, the 
same distance ; or, a ball of one pound weight, moves twice as 
fast as a ball of two pounds weight, if both are impelled by the 
same force. Again, if two balls of equal weight are impelled, the 

* The apple being detached from the tree by the momentum of the 
stone, is brought to the ground by a new power, viz., gravitation. 

150. Resistance of rest. 

151. The resistance of motion. 

152. Second law of motion. 

153. Motion in the direction of the force impressed. 

154. Motion proportioned to the force which produced it. 



46 NATURAL PHILOSOPHY. 

one with a force twice as great as the other, the quantity of mo- 
tion of the one, will be twice as great as that of the other. A man 
by exerting his strength, might with a rope, draw a small skiff to 
shore very quickly ; a loaded barge would, with the same force, 
move slowly, and a large ship with scarcely a perceptible motion. 

155. Third law of motion : to every action of one body upon 
another, there is an equal and contrary reaction ; or, when a body 
communicates motion to another, it loses of its own momentum as 
much as it imparts. 

156. If a man in one boat, pull at a rope attached to another, 
his own boat will be moved by the force which he uses ; if the 
two boats be of equal size and load, they will both move at the 
same rate, and meet half way from the places from which they 
started. If a man in a small boat, should attempt to pull towards 
him a large ship, his own boat would move with a velocity, greater 
in proportion, as its weight is less than that of the ship ; but if in 
a large ship he should draw towards him a little boat, the ship 
itself would be reacted upon, and move, although not enough to 
be perceptible to the senses. This may be the better understood, 
by supposing that if the resistance of the ship were one thousand 
times greater than that of the boat, a thousand men in as many boats, 
all pulling together in one direction, would cause the ship to meet 
them halfway. A boatman pushes off his boat by pressing with 
his oar against the land, the force reacting in the opposite direc- 
tion ; by a continued succession of back 

Fig. 28. strokes, and the reaction of the water 

upon the boat, it is moved forward. 
The bird flies upward, by striking the 
air with its wings in a downward direc- 
tion ; the air reacting upon his body, 
raises him at each stroke. In flying 
through the air in a horizontal direc- 
tion, the stroke with his wings would 
be backward, like the strokes of a boat- 
man with his oar. 

157. A man in swimming, by striking the water downward and 
backward with his hands, is borne upward and forward by the re- 
action of the water. The cripple setting his crutches upon the 
ground, receives a reacting force in his arms, which thus perform 
part of the labor of walking. 

158. The third law of motion may be illustrated by the percus- 

155. Third law of motion. The force which produced it. 

156. Examples illustrating the third law of motion. 

157. Further examples — swimming— walking on crutches. 

158. How may the third law of motion be illustrated ? Percussion. Elas- 
tic bodies. 




<;ka\it\t. 



47 



sion of elastic and non-elastic bodies. By percussion, is meant 
the collision, or striking together of bodies. Elastic bodies, are 
those which, after compression, return to their former state. If 
bodies have the power of restoring themselves immediately after 
compression, or possess a force equal to any compressing power, 
they are said to be perfectly elastic. Air is an example of this ; 
a bladder filled with air, after being compressed, will immediately 
expand to its former bulk. Solid bodies which will retain no per- 
manent bend, are highly elastic, as marble, steel, and glass. A 
o-ood steel sword may be bent until its ends meet, and yet return 
to its former state on being released from the force by which it 
was bent. Bad steel is not thus elastic, but will break in bend- 
ing. A pane of glass may be bent, but will instantly spring 
back. Indian rubber is highly elastic, though not perfectly so, 
for after being frequently stretched, it will appear to have lost 
something of its power to resume its former state. A ball of 
wool, cotton, or sponge when compressed, exhibits the property 
of elasticity. 

159. When two perfectly elastic bodies, of equal weight and ve- 
locity, strike against each other, the striking 
body communicates the whole of its motion to 
the other, and then remains at rest. 

Suppose two ivory balls a b, of equal weight, 
be suspended by threads ; let a be drawn 
aside to c, and then let fall against b, it will 
drive it to d, or a distance equal to that through 
which a had fallen, while the latter, having 
imparted all its motion, remains at rest, 
at a. 

160. Or, suppose a number of 
ivory balls of equal weight to be 
suspended by threads, and the ball 
a be drawn aside and then suffer- 
ed to fall against b, the latter will 
communicate its motion to c and 
then stop ; c will in like manner 
communicate its motion to d, and 
thus each ball will successively 
transmit its motion to the next, 
and remain at rest, while the last ball/", will move off to B w r ith 
the original velocity of a. 



Fig. 29. 




Fisr. 30. 



b c d e f 




B 



159. 
160. 



Two elastic balls striking against each other. Example. 
Motion communicated to several elastic balls. 



48 



JVATURAL PHILOSOPHY, 



161. The elasticity of bails of ivory and marble may seem 
doubtful, since they cannot be compressed with the hand, like an 
indian rubber or cotton ball. But an ivory letter- folder, or riding- 
stick, is manifestly elastic, since, when bent, it springs back as 
soon as the force is withdrawn. That both ivory and marble do 
yield by collision, is proved by a very simple experiment. If an 
ivory ball fall upon a marble slab, owing to the elasticity of both 
bodies, it will rebound nearly to the height from which it fell, and 
there will be no visible mark of any compression of either body ; 
but let the marble slab be wet, and from the fact that a circular 
surface? of some extent, is found dried by the blow, it will be seen 
that both bodies had yielded at the point of contact. Billiard balls 
retain their perfect form, and even their polish, for a long time, 
although they are, in reality, indented at every stroke ; but, from 
their great elasticity, the compressed parts instantly spring back. 
Sealing wax retains the impression of the seal because it has no 
elasticity, or power to spring back after the resistance is removed. 
Figures can be stamped on soft clay, and unleavened dough, for 
the same reason. In raised dough, owing to its pores being filled 
with an elastic fluid,* there is much elasticity. 

162. If an elastic body fall upon an immovable obstacle, it will 
rebound with a force equal to the stroke, and in a contrary direction ; 
thus exemplifying the third law of motion, that action and reaction 
are equal, and in contrary directions. 

163. If a ball of ivory, or any other elastic substance, be dropped 
perpendicularly upon a marble slab, or other hard, immovable body, 
it will rebound in the same straight line in which it fell ; but if 

thrown obliquely, it will not rebound in the 
same line by which it first moved, but as 
obliquely, on the opposite side. Suppose an 
elastic ball a, to fall upon a hard substance b ; 
if it fall perpendicularly, or in the line a b, it 
will rebound in the same perpendicular, or in 
the line b a ; but if it falHn the direction c b, 
it will rebound in the line b d. Now c b is 
the line of incidence.^ and d b is the line of 
reflection,^, and the more oblique or slanting 
the former line is, the more so will be the latter. The perpen- 

* Carbonic acid gas. 

t Incidence, from the Latin incidens, falling upon. 

X Reflection, from the Latin re and fiecto, signifying to throw back. 




161. Ivory and marble proved to be elastic. 

162. An elastic body falling against an immovable object. 

163. Elastic balls falling perpendicularly. Angles of incidence and re- 
flection equal. 



OF THE PROPERTIES OP MATTER. 



49 



Fig. 32. 

I 




dicular line a b* divides the angle made by the lines of incidence 

and reflection into two parts or 
angles, and these angles are equal ; 
from whence it follows, that the 
angle of incidence is always equal 
to the angle of reflection. The 
boy who throws his ball upon the 
pavement, may chance to see a 
glass window broken by its re- 
bound, if he disregard this law of 
reflection. Sound and light are re- 
flected in the same manner as solid 
elastic bodies. 
164. Non-elastic bodies, are those 
which are destitute of the elastic spring. When one non-elastic 
body strikes another, the bodies do not rebound as in the case 
of elastic bodies. Lead, dough, moist clay, &c, are non-elastic. 

165. Suppose a and b, to be two non-elastic 
balls, suspended at c by threads of equal 
length, so that they may be in contact when 
at rest ; and let d e be a graduated arc over 
which the balls may move ; then if the ball b, 
be moved a certain number of degrees towards 
e, and let fall so that it will strike the ball a, it 
will communicate to the latter, half its momen- 
tum, and both balls will move towards d, through 
a number of degrees proportioned to their com- 
mon velocity ; that is, half as far as the ball b 
would have moved if it had met with no ob- 
struction ; but as the two balls, containing 
twice the quantity of matter, are now moved by the same force 
which impelled b, it follows that the velocity is diminished by one 
half. 



Fig. 33. 




B 



D * It may be well here to explain, that 
though, in general, we mean by a per- 
pendicular line, one that falls in aright 
line toward the center of the earth; in 
geometry, any line which makes right 
angles with another line is said to be a 
perpendicular line ; and in this sense, 
the line A B, falling upon C D, or the 
wall of an apartment, is a perpendicular line, although, commonly speak- 
ing, a line in that direction would be horizontal. 



164. Non-elastic bodies. 

165. A non-elastic body in motion falling against one at rest. 

5 



50 NATURAL PHILOSOPHY. 

166. If two non-elastic bodies of equal weight and velocity strike 
against each other, the momenta of both will be destroyed. Suppose 

that the two bodies, A B, 

fig. 34. have equal weight and 

velocity, and of course 

equal momenta ; moving 

C in opposite directions 

they meet at C, by which 

stroke the momenta of 

both balls are destroyed, 

and they remain at rest, 

as seen at D and E. 

If a non-elastic body strike upon an immovable obstacle, it 

will lose all its motion. For example, let a ball of lead, or of soft 

clay fall upon the floor, and it will stop without any rebound. 




LECTURE VII. 



COMPOUND MOTION. COMPOSITION AND RESOLUTION OF FORCES. 

167. A stone thrown by the hand, or a ball shot from a gun, 
is generally considered as an example of simple motion, though even 
here, the force of gravity is in operation. Strictly speaking, there 
is no case of simple motion, since, in the absolute motion of all ter- 
restrial bodies, is combined that of the earth, in its diurnal and an- 
nual revolutions. 

168. Compound motion is that which is produced by several forces 
acting in different, but not in opposite directions. 

169. If forces be equal, and their directions exactly opposite to 
each other, the body acted upon will not move at all. 

170. When two forces (not in direct opposition) act upon a body 
at the same time, as it cannot move two ways at once, it holds a mid- 
dle course between the directions of the separate forces. This 
course is called the resulting direction, or resultant, because it re- 
sults from the composition or union of the forces. 

166. Meeting of two non-elastic bodies in motion. 

167. Simple motion, 

168. Compound motion. 

169. Equal and opposite forces. 

170. Resulting direction. 



COMrOUND MOTION. 



51 




D C 



is a square, 



Fig. 36. 



171. Suppose a ball A, to be at the same 

Fig. 35. instant struck by two equal forces X and Y, 

Y the former moving in the direction B, and the 

latter in the direction C ; the force X alone 

would carry the ball to B, and the force Y 

would carry it to C ; but the joint action of 

the two forces will cause it to move in a 

diagonal line at an equal distance between 

them. If you draw a line from B, parallel 

to A C, and another from C parallel to A B, 

(he two lines will meet in the point D, where 

the ball would stop. The figure A B 

and the line D A is the diagonal of a 

square. 

172. In the example above given, the moving forces were equal. 
But suppose the force X to be twice as great as the force Y, it 

would drive the ball twice as far, con- 
sequently the line A B, (the distance 
to which the ball A would be driven 
by the force X) would be twice as 
long as the line A C (the distance to 
which the ball would be driven by the 
force Y.) The body, acted upon by 
the compound forces, would move in 
a diagonal line between the two ; and 
by drawing a straight line from B, parallel to A C, and another 
from C, parallel to A B, they will meet in the point D, and the 
line D A is the diagonal of a parallelogram, whose length is double 
its breadth. 

173. Different forces act with greater power upon a moving body 
when the angle at which they meet is acute, as they approach nearer 
to a union of forces, hence the diagonal or resultant will be 
longer, as may be seen in Figure 36. By rendering the angle 
BAG more acute, the diagonal or resultant would be longer, be- 
cause the joint impression of the forces would be increased ; there- 
fore when this angle should entirely disappear, or in other words, 
when the sides A B and A C should coincide with the diagonal 
A D, the two forces would act in the same direction, and the 
moving body have the full effect cf their joint forces ; but this 
would cease to be an example of the composition of forces ; it 
would be the complete union of two forces. 

174. Again, if the angle made by the direction of two forces be 




171. Example of motion caused by two equal forces. 

172. Motion caused by two unequal forces. 

173. Compound forces acting at an acute angle. 

174. Compound forces acting at an obtuse angle. 



52 



NATURAL PHILOSOPHY. 



Fig. 37. 





B 



obtuse, as in the angle BAG, (Fig. 37,) they approach to an op. 
position of forces ; and the diagonal or re- 
sultant A D is proportionally shortened. 
When the forces represented by the lines 
A B and A C, meet without forming any 
angle, provided they are equal forces, they 
act in direct opposition, and destroy each 
other, consequently a body acted upon at 
A, would have no motion. But if one 
force be superior to the other, the body 

does not move in a diagonal line, but in the direction of the 

greater force. 

175. When a body would describe the two sides of an equilateral triangle 
by two forces acting separately, it will, in the same time, describe an equal 

side, by the two forces acting joini- 

■p- eg ly. Thus a boatman wishing to 

o" * cross a river, from A to C, would 

steer his boat directly towards B, 

so that his own force combined 

with the force of the stream acting 

from E to A, or B to C, would cause 

the boat to describe the diagonal A 

C. The force of the stream alone 

would carry him from A to D, his 

own force alone, would, in the 

same time, carry him to B ; but the 

two forces compounded, will carry 

him to C, in the same time as the one force would have carried him to D, or 

the other to B.* 

176. When the circus rider leaps over a rope, as his horse is 
galloping at full speed, he comes down upon the saddle, descend- 
ing not in a perpendicular, but an 
oblique direction, rising in one diag- 
onal line and descending in another. 
If the horse were standing still, the 
motion of the rider in leaping up, 
would carry him from A to B, but 
the motion of the horse alone would 
carry him directly forward ; the di- 
agonal between the two forces is the 
line A G, by which he would rise, 
while he would descend in the diag- 
onal G D, through the joint effect of the force derived from the 

* By a reference to Fig. 31, with the explanation, the pupil will easily 
comprehend how the parallelogram A B C D is obtained, and will perceive 
that the short diagonal A C, is made by the obtuse angle BAD, according to 
the illustration of Fig. 33. 

175. What proposition does Fig. 34 illustrate? 

176. What case affords an experimental illustration of the parallelogram 
of forces ? 



Fig. 39. 




COMPOUND MOTION. 



53 



Fig. 40. 



motion of the horse and his own weight, the former of which 
would tend to carry him from G to C, while the latter, alone, would 
impel him from G towards H. This case affords an experimental 
illustration of the parallelogram of forces ; the sides of the paral- 
lelograms A 15 G II, and GHCD represent the quantity and di- 
rection of the two forces acting together. 

177. A stone dropped from the mast-head 
of a vessel under sail, being affected by the mo- 
tion of the vessel as well as by the force of 
gravitation, would not fall in a perpendicular, 
but in a diagonal line. Let A represent the 
mast, S the stone, D the deck, and the line S 
E will be the distance that the mast-head will 
have moved, while the stone Avould have fallen 
from the force of gravity alone, from S to the 
point under it on the deck ; but the stone, par- 
taking of the common motion of the ship, and 
impelled by gravity, takes a diagonal direction, 
in the line S B. 

178. The navigator, in crossing the ocean, by observ- 
ing the course of his ship, is able to determine the lati- 
tude and longitude. Thus if the course of his ship, ac- 
cording to observations made with the mariner's com- 
pass, has been, for a certain time, south-west, let D A and 
B C represent parallels of latitude, and D B and A C par- 
allels of longitude, the diagonal line A B will describe 
the ship's course through the sea, and the difference of 
latitude and longitude at particular points of the vessel's 
track may thus be estimated. 



VI 



Fig. 41. 




Motion resulting from more than two forces. 



I 






179. Bodies may be moved 
by the action of more than two 
forces : A kite, in flying, is acted 

7c L f/.^:~/32\ s M u pon by three forces, the string, 

the wind, and gravity or, (which 
is the same thing,) its own 
weight. The boy, to make 
his kite rise, first balances 
l/s \ s it in an oblique position in the 

£l\ air, then runs with it a few 

rods, that the air, by its reaction, may throw it upwards. Let 

177. Would a stone dropped from the mast head of a vessel under sail, 
fall in a perpendicular line ? 

178. Course of a ship indicating latitude and longitude. 

179. How many forces is a kite flying, acted upon ? In how many direc- 
tions is it acted upon 1 

5* 



51 NATURAL PHILOSOPHY. 

a b represent a kite in the air, in a slanting position, or inclined to- 
wards the surface of the earth, at an angle of 45 degrees,* and let 
d s represent the string. Suppose the wind to be blowing in the 
direction w d ; when it strikes the kite at d in the line d h, it will be 
reflected in the direction d g ; and the force of the reflected wind, re- 
acting on the kite in the opposite direction, will tend to carry it per- 
pendicularly towards h ; but the wind is also acting on the kite with 
direct force in the line w d, tending to carry it horizontally towards 
k, while gravity is tending to bring the kite to the ground, in the 
perpendicular direction, d g. It is then acted upon in three direc- 
tions, upward toward h, by the reaction of the reflected force of the 
wind, sideways, or toward k by the direct force of the wind, and 
downward, or toward g, by gravity, 

180. Suppose the weight of the kite pull it downward with the 
force of two pounds, and the wind act upon it upward, with a force 
equal to two pounds, and horizontally with the same force, it is 
evident that it will move horizontally ; since the two forces, d g 
and d h, acting in opposite directions, would destroy each other, 
and leave the kite to be moved wholly by the force w d. 

181. But if the forces be unequal, the weight of the kite being 
but two pounds, while the horizontal, and upward force of the wind 
are each equal to four pounds, the kite would then be impelled 
horizontally toward k with a force of four, and upward toward h 
w T ith the force of two pounds (half the upward force being lost by 
the opposing weight of the kite) ; now, let the line d k be made 
twice the length of d h to represent double the force ; then com- 
plete the parallelogram dhlk, the diagonal d I will represent 
the line in which the kite would move. 

182. By letting the string of the kite fall from the hand, the re- 
sistance which it had offered to the w r ind would cease, and when 
this resistance no longer existed, there could no longer be any re- 
flected motion ; and the kite after being blown along by the horizon- 
tal action of the wind, would be brought to the earth by gravity. 

* A B represents the surface of the 
earth, C the zenith or point directly 
over head, a line drawn from which 
makes, with the surface of the earth, 
the angle C E B, or an angle of 90 de- 
grees. The line D E forms with the 
same, the angle D E B, of 45 de- 
grees. 



180. When would a kite be made to move horizontally? 

181. What would change the horizontal motion into a diagonal, upward 
motion 1 

182. Effect of letting the string of the kite loose. Effects of the wind 
upon the motion of the kite. 




COMPOUND MOTION. 



55 



Fig. 43. 



By holding the string very tight, the horizontal force of the wind 
ceases to act upon the kite, and the reflected force raises it per- 
pendicularly. When a kite rises suddenly in a perpendicular di- 
rection without the string having been pulled, it is because its re- 
flected force is increased by an increased velocity of the wind ; 
when the kite descends without any slackening of the string, it is 
owing to a lessened force of the wind, or to a change in its di- 
rection. 

183. The combined effect of three or more forces acting on a body in dif- 
ferent directions, may be discovered by means of the parallelogram of forces ; 
and a single force may be thus assigned which will be the resultant of those 
forces. This may be done by obtaining first the diagonal, representing the 
resultant of the combination of two forces, and considering that diagonal as 
the side of a parallelogram, of which a line representing a third force will 
form one of the other sides, and the parallelogram being completed, the di- 
agonal will be the resultant of the first three forces; and the operation may 
be extended in the same manner so as to discover the ultimate resultant of 
any given number of forces. 

Let the point A be impelled by forces in the 
directions A B, A C, A D, and A E ; then, to 
find out the resultant of these combined forces, 
complete the parallelogram C A B F, and the 
diagonal A F will exhibit the result of the forces 
A B and A C. Complete the parallelogram D 
A F G, and its diagonal A G will denote the re- 
sult of the three forces A B, A C, and A D. In 
the same manner, complete the parallelogram 
EAGH, and the diagonal A H will represent 
the force compounded of all the four forces, A 
B, A C, A D, and A E. But the construction 
may be simplified by merely drawing the lines 
B F, equal and parallel to A C ; F G correspond- 
ing with A D; and G H, bearing the same relation to A E; then, the line 
Joining A and H, which as before will express the resulting force. 

It may be demonstrated by means 

Via 44- °^ tne parallelogram of forces, that 

°* ' from three forces acting in the di- 

C rections A B, A C, and A D, in the 

E proportions of the length, breadth 

and depth of a parallelopiped,*' will 

result a motion in the diagonal A 

F of that parallelopiped ; for A B 

and A C compose A E, and A E and 

A D compose A F ; which last is the 

resultant of the moving forces in 

the directions of the three sides of 

the parallelopiped. 

The effect of the composition of forces, when a body impelled in different 

directions takes the course in a diagonal line between the two impelling 

forces, may be thus experimentally exemplified. 








y 


H 




B 


^/L 




X7 



* A parallelopiped is a regular solid comprehended under six parallelograms, the oppo- 
site ones of which are similar, parallel, and equal to each other. 



183. Parallelogram of forces. Explain Fig. 43. Explain Fig. 44. 




56 NATURAL PHILOSOPHY. 

LECTURE VIII. 

ACCELERATED AND RETARDED MOTION. 

184. Uniform motion, is that, by which a 
Fig. 45. body passes over equal spaces in equal times ; 

as the minute hand of a watch or clock, 
which, in sixty minutes, passes through a 
given circle. The hour hand has also a uni- 
form motion, though much slower, since it 
passes through the twelfth part of the circle 
only, while the minute hand passes through 
the whole ; — the relative velocity of the hour 
hand is, therefore, twelve times less than that 
of the minute hand. 

185. A body once set in motion, would continue to move for- 
ever with uniform velocity, but for the resistance of the air, fric- 
tion, gravity, &c, from the influence of these causes, there must 
be, in order to produce uniform motion, the constant exertion 
of a uniform force. 

186. The uniform motion of a watch is produced by a force (the 
spring) acting upon the wheels, in a steady and uniform manner. 
A horse, moving at the rate of six miles an hour, goes with a uni- 
form velocity, caused by the continued exertion of muscular strength. 

187. A body descending by gravity is not acted upon, by one 
impulse merely, but by a continued series of impulses, each added 
to the previous ones. If a ball rolling upon smooth ice were eve- 
ry instant to receive a new stroke, retaining all the previous mo- 
mentum and continually receiving more, its velocity would soon 
become very great. Thus a falling body is continually receiving 
new velocity and momentum from gravity. 

Spaces described by Falling Bodies, 

188. The spaces described by bodies falling from a state of 
rest by the influence of gravity, are as the squares of the times, 
during which, they are falling. 

A stone falling from a high tower, will, in two seconds, fall 
four times as far as in one second ; in three seconds, nine times 
as far ; in four seconds, sixteen times as far ; and in ten seconds, 
one hundred times as far ; because the square of 2 seconds is 4, 
of 3 is 9, of 4 is 16, and of 10 is 100 seconds. 

184. Uniform motion. 

185. What is necessary to produce uniform motion ? 

186. Examples of uniform motion. 

187. Falling bodies continually acted upon by new impulses. 

188. Proposition concerning the relation between the spaces and limes of 
falling bodies. 



ACCE'LEKATKI) AND RETARDED MOTION. 



57 



189. It has been proved by experiments, that a body falling from 
a state of rest, passes through 16 feet* the §rst second of time ; in 
two seconds, it passes through 4 times 16, or 64 feet ; and in three 
seconds (multiplying by 9, which is the square of 3), it passes 
through 144 feet ; and in ten seconds (multiplying 10 by the square 
of 10), 1600 feet. Therefore, to find the number of feet through 
which a body has fallen, the time being known, multiply the 
square of the number of seconds by 16. The spaces being pro- 
portioned, not simply to the times 1, 2, 3, and 10, but to the 
squares, 1, 4, 9, and 100. 

Ex. Suppose a body to have been falling 5 seconds ; through 
what space has it fallen ? Ans. 400 feet. 

Velocity of Falling Bodies, 

190. If a body, having fallen through a certain space in a given 
time, should receive no farther impulse from gravity, but proceed 
on, uniformly, with the last acquired velocity, it would describe 
twice the space through ivhich it had passed, in the same tune 
as that, during which it had fallen to acquire that velocity. 

Ex. Suppose a body, at the end of one second, to have fallen 16 
feet, it would have acquired a velocity which in the next second would 
carry it 32 feet ; at the end of four seconds, its space, multiplying 
16 by the square of 4, being 256 feet, the next four seconds it 
would descend 512 feet, or twice the space in the same time as that 
during which it had fallen to acquire that velocity . 
Time, Space and Velocity. 

Fig. 46. 191. The line A B represents the time 

A in which a falling body descends, di- 

vided into seconds ; the horizontal lines 
1 C, 2 D. 3 E, 4 F, and 5 G, represent, by 
their increasing lengths, the velocity ac- 
quired in each second. The small trian- 
gles represent spaces. By multiplying 
16, the number of feet in which a body 
falls the first second, by the number of tri- 
angles in each line, we learn the space 
passed through in each second. In the 
first second we have 1 triangle a ; in the 
next second we have 3 triangles b c d ; in 
the third second we have 5 triangles, e f g, 
&c; in the fourth second we have 7 trian- 
gles, j k I, &c; and in the fifth second we 

* 16 feet and one inch, is the exact distance through which, it is proved, a 
body falling freely by gravitation, passes, the first second of its descent. 

189. Allowing that a falling body would pass through 16 feet the first sec- 
ond of time, how far would it fall in ten seconds 1 Ex 

190. Proposition with regard to the motion of a body proceeding with the 
last acquired velocity. Ex. 

191. Explain the diagram representing time, space, and velocity. 



1 

2 




!'C\ 


D ''\ 








3 


1 \ 




E.\i '*••-. 




4 




11 \ 




•\ 


F \ 




5 








\ 7* 

.9 \ 


\ 


G 



58 



NATURAL PHILOSOPHY. 



have 9 triangles, q r s, &c, the spaces in each successive second increas- 
ing in proportion to the series of odd numbers, 1, 3, 5, 7, 9, &c. That is, 
during the first second, the body falls a certain distance, say 16 feet ; during 
the next second it falls three times as far; during the third, Jive times as 
far; during the fourth, seven times as far ; during the fifth, nine times as 
far, and so on in the same proportions. The odd numbers, 1, 3, 5, &c. are 
the ratios or proportions in which the velocity of falling bodies is uniformly 
accelerated. 

192. Rule. — If a body fall 16 feet the first second, in the second 
second it will fall 48 feet, or 16 multiplied by 3 ; in the third second 
it will fall 80 feet, or 16 multiplied by 5, &c. 

Through how many feet would a body descend the fifth sec- 
ond of its fall? Ans. 144. We multiply 16 by 9, because 
the body falls nine times as far during the fifth second, as the 
first. 

193. If it be required to find the whole space through which a 
body has fallen during five seconds of time, multiply 16 by the 
square of the time ; the square of 5 being 25, the answer would 
be 400 feet. 

194. The following Table may illustrate this subject : 



Seconds of de- 


Feet passed through at the 


Final velocity in each 


Feet passed through 


scent. 


end of each second. 


second. 


during each second. 


1 


16 


32 


16. 


2 


64 


64 


48. 


3 


144 


96 


80. 


4 


256 


128 


112. 


5 


400 


160 


144. 



The first cohimn of figures stands for the time of descent of a falling body, 
as divided into seconds. 

The second column of figures shows the whole number of feet through 
which the falling body has passed at the end of each second ; these num- 
bers are obtained by multiplying 16 by the square of the figure in the first 
column, according to the following rule: the whole spaces passed through 
are proportional to the squares of the whole times. 

The third column of figures shows the final velocity in each second; these 
numbers are obtained by multiplying 16 by the even numbers 2, 4, 6, 8, &c, 
according to the following rule : the velocity passed at the end of any number 
of seconds, is represented by twice that number multiplied by 16 ; as the final 
velocity at the end of two seconds is 64, or 16 multiplied by twice 2. 

The fourth column of figures shows the feet passed through during each 
second ; the numbers are obtained by multiplying 16, by the series of odd 
numbers which represent the ratio of acquired velocities, according to the 
following rule : the spaces through which a falling body passes in a succession 
of equal intervals are in the proportion of 1, 3, 5, 7, 9, 11, &c. ; the number 
of feet passed through in each second is 16 less than that of the final velocity ; 
that is, the body has acquired during the last second of its fall a velocity 



192. If a body fall 16 feet the first second, how many will it fall the sec- 
ond and third seconds ? How many the fifth second ? 

193. How can you find the whole space through which a body has fallen 
during five seconds ? 

194. Explain the table. The first column of figures. The second column 
of figures. The third column of figures. The fourth column of figures. 






ACCELERATED AND RETARDED MOTION. 59 

which, without any new impulse from gravitation, would, in the next second, 
it 16 feet farther than it moved the preceding second. 

195. The spaces described by falling bodies,* are proportioned to the 
IQ1 ires OF THE VELOCITIES which the;/ acquire, in falling over those spaces. 

Rule. — Divide (he square of the velocity by 64. 

Ex. If a ball, falling from the summit of a tower, acquire a velocity 
of 80 feet, what is the height of the tower? Ans. The square of 80 is 6400; 
which divided by 64, equals 100 feet, the height of the tower. Ans. 
iM<2-+- 64 = 100. 

196. In all computations respecting the velocity of falling bodies, 
the essential points are, to know the space fallen through in one 
second, and the acquired velocity during that time. The height 
of a tower or precipice, or the depth of a well or cavern, may be 
easily computed by marking- the time in which a body falls from 
the top to the bottom ; or if the height or depth be known, the 
time in which a body would fall to the bottom maybe ascertained. 

Ex. If a stone let fall from the top of a well, is 4 seconds in 
reaching the bottom, what is the depth of the well 1 

Multiplying the square of the number of seconds by 16, we 
find the depth of the well to be 256 feet : for the square of 4 
is 16, which, multiplied by 16, equals 256 feet ; therefore, 
4 2 X 16 = 256 ft. 

197. Though the resistance of the air in impeding the velocity 
of falling bodies, has not been calculated in our computations, this 
has some effect, even in the case of the heaviest substances. By 
the expression, " a body falling freely by gravitation" is to be 
understood, a body falling in a vacuum. It is proved, by the ex- 
periment of a piece of lead and a feather falling in an exhausted 
receiver, that the velocities of all bodies falling, in a vacuum, from 
the same height, are equal ; as the attracting force which acts 
upon the greater mass exceeds that which acts upon the less, as 
much as the greater body exceeds the less, in quantity of matter. 

* A body moves 16 feet during the first second, and 48 during the next sec- 
ond, therefore it acquires a velocity of 32 feet in passing over 16 feet; hence 
the square of the acquired velocity or (32) 2 bears the same ratio to the space, 
viz. 16 feet, that the given"acquired velocity bears to the required space. 
Let 40 feet be the acquired velocity, then we shall have the proportion 
(32) 2 : 16 : : (40) 2 is to the required space. Since the first term of this pro- 
portion or (32)2 __ (i(j x 2)2 = 22 X 16 X 16, we can divide the terms of 
the first ratio by 16, and the proportion becomes 22 X 16 : 1 :: 40 2 is to 
the required space, as 2 2 X 16 = 64, hence, 64 : 1 : : 40 2 is to the required 
space, 40 2 = 1600 -~ 64 = 25 feet. From this we derive the following 
rule, for finding the spaces described by falling bodies when the acquired 
velocity is known. 

195. Proposition concerning the spaces described by falling bodies. Rule. 
Ex. 

196. Essential points in computing the velocity of falling bodies. Ex. 

197. What is meant by bodies falling freely? When are the velocities 
of all bodies, falling from the same height, equal? 



60 



NATURAL PHILOSOPHY. 



Fig. 47. 



198. The accelerated motion of falling bodies is familiar to every observer 
of nature: — an apple falling from the top of a high tree, is at first visible to 
the eye, but it soon acquires so great velocity, as to render it indistinct to the 
sight, and only the line of its descent is visible. Let a fragment of a rock be 
pushed from the height of a precipice ; at first its speed is not very great, but 
it soon begins to move more rapidly, and gathering new velocity at every in- 
stant of its fall, it rushes downward with tremendous force. Boys accustomed 
to slide down hill upon their little sledges, are familiar with the fact that the 
velocity acquired in their descent, carries them on some distance after they 
have reached the foot of the hill, and even some way up an acclivity. When 
standing by a waterfall of considerable height, we may first see the water 
slowly descending in one sheet, but as the eye follows its downward course, 
we perceive the force and velocity becoming greater at every instant, until, 
seen only as foam or mist, it dashes into the chasm below and mingles with 
the current. 

199. Calculations respecting falling bodies have 
been rendered very accurate by Attwood's* ma- 
chine, by means of which the descent of falling 
bodies is made so gradual, that the relations 
between times and spaces, can be accurately de- 
termined ; for though the motion is retarded, these 
relations remain unchanged. The machine con- 
sists of a wooden column about ten feet high, with 
a rod marked by feet and inches, and two weights 
suspended over pulleys. The rapidity of the fall- 
ing motion in the heavier weight is retarded by the 
lighter weight ; thus the increase of velocity is so 
gradual that it may be seen by the naked eye, as 
the weight descends along the graduated rod, while 
the seconds of time may be noted by listening to 
the beats of a clock attached to the machine. 



Retarded Motion. 



200. The ascending motion of bodies thrown up- 
ward, is retarded in the same proportion as the mo- 
tion of falling bodies is accelerated. The same 
laws that regulate uniformly accelerated velocities, 
apply equally to uniformly retarded velocities, the 
motions being reversed. 




* George Attwood was Professor of Natural Philosophv, at Cambridge, 
England, in 1784. 



198. Examples of accelerated motion. 

199. The size and construction of Attwood's machine 

200. In what proportion is upward motion retarded ? 



CURVILINEAR MOTION. PROJECTILES. 01 

Fig. 48. 201. Suppose that a body thrown from A, perpen- 
dicularly upward, moves with a force sufficient to carry 
it, in the first second to B, in the second to C, in the 
third to i), and in the fourth to E, the motion, which has 
been, uniformly, growing less, here ceases, and gravity, 
having nt>w wholly overcome the projectile force, ope- 
rates without opposition. The body begins to fall, and, at 
every instant, receiving from gravity a new momentum 
downward, passes through the same spaces in the same 
times, as in its ascent ; that is, it falls from E to D in 
the first second, from D to C in the next, from C to B 
in the third, and from B to A in the fourth. 

202. The projectile force is that which impels the 
body ; it may be greater or less, as a bullet thrown 
upward with the hand, moves with little force compared 
with the momentum of a bullet shot upward with a 
gun. In the former case, the velocity would be less 
than in the latter, in proportion as the projectile force 
was less ; the space through which it would move would 
be less in the same ratio, as would also be the time 
which would pass before it reached the ground. If one 
body be shot upward with twice the force of another, it 
will rise twice as high ; if shot with ten times the force 
it rises ten times as high. 

203. Suppose an arrow shot upward from a bow fell 
to the ground in six seconds, how many feet did it 
ascend ? Ans. The times of ascent and descent being 



B — 



equal, the arrow was three seconds in rising, and three in falling. 
It, has been shown that, in order to know the spaces described by 
a falling body, we must multiply the squares of the time by the 
velocity, which in bodies falling by gravitation, is 16 feet the first 
second ; the square of (the number of seconds in which the ar- 
row was falling) is 9 ; this multiplied by 16 gives 144, which is 
the number of feet the arrow fell ; consequently it must have risen 
to the same height, that is 144 feet. 



LECTURE IX. 

CURVILINEAR MOTION. PROJECTILES. 

204. Curvilinear Motion, or motion in curved lines, is the result 

201. Explain Fig. 48. 

202. On what does the velocity of a projectile depend ? 

203. To what height must a body have ascended which falls to the ground 
in six seconds after it was thrown upward 1 

204. Cause of curvilinear motion. Stone whirled in a sling. Ball revolv- 
ing in a hoop. 

6 



oz 



NATURAL PHILOSOPHY. 



of two forces acting on a body ; by one of which it is projected 
forward in a right line, whilst by the other, it is drawn or impelled 
towards a fixed point. When either of these forces ceases to act, 
the body will move in a straight line. A stone whirled in a sling, 
is acted upon by two forces, that of the hand, which represents 
the projectile force, and that of the string, which causes it in its 
motion to describe the circumference of a circle ; but if the string 
break while the stone is thus whirling, the stone would fly off in 
a tangent, being then acted upon only by the projectile force. 

If a ball be made to revolve within a hoop laid flat upon a ta- 
ble, it will manifest a constant tendency to escape from a circle 
in which it is moving, by pressing against the sides of the hoop. 
It is evident that if the hoop be lifted up while the ball is re- 
volving, the circular motion will be destroyed and the ball fly 
off in a right line from the point where it is set free ; and this 
line will form a tangent to the circle in which the ball had 
moved. 

205. Thus we find curvilinear motion to be produced by two 
antagonist powers ; the one, which draws the moving body towards 
the center of motion is called the centripetal* force, and the other, 
which is constantly tending to drive it from the center, is called the 
centrifugal,]' and sometimes the tangential force, because the line 
of its direction is that of a tangent to the circle. These two forces 
are also called, central forces, 

206. Motion in a circle is, at every successive instant, a bent 
motion ; for a circle is made up of an 
infinite number of straight lines, and a 
constant force is necessary to counter- 
act the tendency of the body to pursue 
these straight lines. 

Suppose a body, a, to be projected 
in the direction a b, and at the same 
time to be attracted with equal force 
by w ; it will obey neither force, but 
move towards d in the diagonal of a 
parallelogram, whose sides a. c, and ap, 
are in proportion to the two forces a b, 
and a w, and whose other two sides are 
obtained by producing j? and c to d. The 
body would now continue to move tow- 

* From centrum, a center, and peto, to tend towards, 
t From centrum, a center, and fugio, to fly from. 



Fig. 49. 




205. Centripetal and centrifugal forces. 

206. Tendency of a body to follow straight lines. Illustrate by Fig. 49, 
the cause of circular motion. Motion of the moon. 



CURVILINEAR MOTION. PROJECTILES. 63 

anls ///, if its motion were not bent by some new force ; but at d, it 
receives a now impulse from w tending to carry it in the direction 
d to, it therefore describes a new diagonal d g, and we have a 
second parallelogram by producing e and f to g. At g, a new 
impulse is received from w, and the body, instead of moving in a 
straight line towards i, describes a new diagonal, g k ; here a new 
impulse from 10, bends the motion from the straight line k n, and 
carries the body on in a new diagonal to o. The line o w is 
shorter than a w, because a, the body acted upon, is supposed to 
receive from w a succession of impulses, while no new action is 
received from b. If we suppose w to be the sun, and a the earth 
impelled in its course by a projectile force at 6, and a centripetal 
force at w, we have the elliptical orbit of the earth, or the path in 
which she moves round the sun. The earth, with this centripetal 
force continually acting and increasing as she approached the sun, 
would be precipitated upon it, but for the law of nature which 
causes an increase of the centrifugal force to follow increased 



Fig. 50. D 



elocity. 



The motion of the moon around the earth, 
is in a curvilinear line, produced by the ac- 
tion of the centrifugal force A D, and the 
\ centripetal force A B ; the latter, which is 
the earth's attraction, operating constantly, 
C causes the moon to describe the curved 
line A C. 

207. The centrifugal force of bodies re- 
volving in a circle, is proportioned to their 
15 specific gravities. Thus, if cork, water, and 

quicksilver be whirled together in a pail, they will arrange them- 
selves in the inverse order of their specific gravities. This ex- 
periment may be performed by suspending the vessel by a cord 
from some fixed point, and twisting the cord by turning the pail ; 
when the cord is let go, it untwists itself, giving a rapid, whirling 
motion to the vessel. This revolution carries the heaviest body, 
viz., the quicksilver, farthest from the center of the vessel or next 
its sides ; the water will be intermediate between the quicksilver 
and the cork, and the cork in the center of the vessel. If the pail 
contain water only, this, by the untwisting of the cord, will sink 
in the center and rise towards the side of the pail, or where the 
centrifugal force is greatest. Thus we see that the centrifugal 
force tends to cause bodies to recede from a central point. 

208. The centrifugal force is increased by increasing the velo- 

207. What causes the elliptical orbit of the earth ? Why is not the earth 
precipitated upon the sun by the superior force of the centripetal power ? 

208. Centrifugal force proportioned to velocity. 



04 NATURAL PHILOSOPHY. 

city of a revolving body ; or, the centrifugal forces are propor- 
tioned to the squares of their velocities. If the velocity be in- 
creased 4 times, the centrifugal force wall be 16 times greater ; 
if increased 10 times, the centrifugal force will be 100 times 
greater. The revolutions of the pail, by the untwisting of the sus- 
pended cord, may be so rapid as to cause a small quantity of the 
water, not only to rise to the edge of the pail, but to be thrown 
off in straight or tangent lines. If a pair of tongs be suspended 
in the same manner as the pail, and made to turn by the untwist- 
ing of the cord, the legs will separate with a force proportioned to 
the velocity of the rotation. When this rotation ceases, they will 
resume their former situation. 

209. An application of the principle above stated to mechanics, is 
seen in the regulator, an important invention for regulating the sup- 
ply of steam, in steam engines. It consists 
of two heavy balls a b, so connected with 
a perpendicular shaft, as to fall parallel to 
the shaft when at rest ; but when they are 
made to revolve by the motion of a com- 
mon axis, the balls diverge by the centri- 
fugal force. By connecting the regula- 
tor at c, with an important part of the 
steam engine called the fly wheel, it is 
made to partake of the common motion 
of the engine ; and, while the motion is 
uniform, the balls will remain at a certain 
distance from the perpendicular shaft. By an increase of steam, 
the motion becomes more rapid ; this causes the balls to diverge 
farther from the perpendicular, and, in so doing, raise a valve con- 
nected with the boiler, by which such a portion of steam is let off 
as will suffer the balls to resume their usual position ; 
Fig. 52. and this position indicates that the velocity of the mo- 
tion is reduced to the rate required. 

210. If a ball of wet clay A, be made to revolve 
jjpjyjji rapidly upon an axis, it expands at the middle, and be- 
'^B A comes flattened at the two ends, as at B. This is be- 
^P^ cause the middle, being farther from the axis of mo- 
tion, has a greater velocity, and, of course, greater 
centrifugal force. The ball A, may be supposed to 
represent the figure of the earth when it first began 
to revolve on its axis, and B to represent its figure as 
it exists at present, elevated at the equator and flat- 

209. Regulator of the steam engine. 

210. Effect of centrifugal force upon the form of a ball of wet clay. Figure 
of the earth. Oblate and prolate spheroids. 





CURVILINEAR MOTION. PROJECTILES. 



65 



Fig. 53. 




tened at the polos.* This figure is that of an oblate spheroid. A 
spheroid differs from a sphere or globe, in being flattened in one di- 
rection, and lengthened in another. An orange is an oblate spheroid. 
A lemon, being elongated towards the ends, is a prolate spheroid. 

211. It has been proved, by accurate calculations, that, if the 
revolution of the earth on its axis were but seventeen times faster 
than it now is, bodies at the equator would be acted upon by cen- 
trifugal force as much as by gravity, in which case they would have 
no weight. A farther increase of velocity would cause them to 
rise and form a ring round the earth, like that which surrounds the 
planet Saturn, or to fly off in pieces which might revolve around 
the earth, like so many little moons. 

212. In order to explain how one part of a 
revolving body moves with greater velocity 
than another, we will illustrate the subject, by 
the motion of a wheel. In each revolution, 
the circle to be described is small in propor- 
tion as it is near the axis of motion or center 
of the wheel, which is, itself at rest ; and, as 
the greater spaces are passed over in the same 
time as the smaller, it follows, that the yelocity 
must be greater in proportion ; and the centrifu- 
gal force increasing with the squares of the velocity, this force must 
be greatest at the rim of the wheel, or where the circle is greatest. 
213. By the axis of motion, is understood a line either real or 
imaginary, round which a body turns. If 
an apple be turned upon a wire passing 
through it, the wire is the axis of motion. 
By the axis of the earth's motion is under- 
stood an imaginary line through its center. 
214. The center of motion, is a point 
round which a body turns, or on which it 
rests, while revolving. Suppose that upon 
the table A D, is fastened a string, C, 
having at one end an ivory ball, B. To 
this ball, a forward motion being given 
with the hand, it is evident that the ball 

* This fact is a strong evidence in favor of the Wernerian theory of geolo- 
gy, or that the materials which compose the earth were once in a fluid state; 
as the globe must have been like the ball of soft clay, in order thus to have 
been flattened at the poles. 

211. Effects which would be produced by an increase of the earth's cen- 
trifugal force. 

212. Velocity least, nearest the center of motion. Centrifugal force great- 
est at the greatest distance from the center of motion. 

213. Axis of motion. Axis of the earth's motion. 

214. Center of motion. 

6* 



Fig. 54. 




66 



NATURAL PHILOSOPHY. 



will revolve in a circle. The force of the hand is the centrifugal 
force, and the confinement in which the ball is held by the string, 
is the centripetal force. The point C is the center of motion. 



PROJECTILES. 



215. Any body thrown, or projected, either obliquely, or hori- 
zontally, is a projectile. Projectiles move in a curvilinear path, 

and the curve which they 
Fig. 55. B describe is called a para- 

bola. Suppose a body to 
be thrown obliquely up- 
ward, in the direction A B, 
the force of gravity will 
immediately begin to draw 
it toward the earth ; and 
as this force is at every 
instant increasing the mo- 
tion of the falling body, it 
will, at every succeeding 
instant, recede more and 
more rapidly from the line 
A B, thus describing the curve A C, which is continually devia- 
ting from the line of projection, until it reaches the ground at C. 
The random of a projectile is the horizontal distance between the 
point from which it is thrown, and that where it falls ; thus the 
line A C, is the random of a projectile thrown in the direction A B. 

The mud thrown from a car- 




Fig. 56. 




riage wheel describes a para- 
bola, as in the lines a c and 
a c ; whereas it would be 
thrown in the straight lines 
a b and a b, were it not for 
the continual action of grav- 

216. Projectile motion does 
not impede the action of grav- 
ity, and hence a cannon ball 
shot horizontally over a level 
plain, will touch the ground 



215. What is a projectile ? A parabola ? What is meant by the random 
of a projectile ? Line described by mud thrown from a carriage wheel. 

216. Does projectile motion impede the action of gravity ? Examples. Ex- 
plain the diagram to demonstrate that a projected body will reach the ground 
at the same instant as one which falls from the same height, and at the same 
time. 



PROJECTILES. 67 

as soon as another ball, dropped at the same instant from the can- 
non's mouth. The body moving forward is going downward at 
every instant, as rapidly, as if it had no other, than the downward 
motion. Suppose one stone to be projected directly forward from 
the top of a high tower t and another, at the same instant, to be 
dropped, directly downward, both stones will reach the ground at 
the same moment. 

If A D be the horizontal line of projection, and A B the per- 
pendicular line of gravitation, then the stone which is projected 
will not move in either line ; but in A C, which is the result of 

the projectile force, and the force 

Fig. 57. of gravitation combined; and it 

would pass through the space A a, 

A r > -.a, I> in the same time that gravity, alone, 

r.3..1.!V;i-].^....., would carry the other stone from 

i X.J^ A to 1. When, therefore, the one 

i\'\ stone is at b, the other is at 2 ; in 

- _ _.i_..\*L.. like manner, c corresponds to 3, 

j \ I d to 4, e to 5, and f to 6. Thus, 

- — - ...L.'if..; the stone which was projected from 

j \j /. A, touches the ground at C, in the 

— L.y.. y me ^ Q f a t the same instant that 

j\j the stone which was dropped 
touches the ground at B. 



B 



217. The study of projectiles is an important part of military 
science. In firing at distant objects, it is necessary that the engi- 
neer should know, not only in what situation to place his can- 
non in order to give the required direction to the ball, but should 
know the velocity with which it will move, that he may thus 
be enabled to calculate the curve it will describe in its transit, 
and, consequently, the spot where it will strike. In cannonading 
a city, a great advantage is gained by an elevated position, be- 
cause projectiles thrown from such a point, take effect at a greater 
distance than if thrown from a level ; as a stone projected from 
the brow of a hill, moves with much greater force and consequently 
over more space, than if thrown by a person standing upon a plain. 
A cannon ball shot horizontally from the top of one of the highest 
points of the Andes, would move three or four miles before striking 
the earth. 



217. Connection of the study of projectiles with military science. 



58 



NATURAL PHILOSOPHY. 



Fig. 53. 



P A 



218. Suppose a body placed at 
the point A, above the surface of the 
earth ; — if it were let fall with no 
projectile force, gravity would cause 
it to descend with an accelerated 
motion toward the earth's center, in 
the perpendicular direction A B. 
But if the body were impelled by a 
projectile force in the direction A P, 
it would descend in the curve line 
A D. The greater the projectile 
force A P, the greater will be 
the sweep of the curve line. A 
greater degree of force would send 
he body to E, and a still greater degree of force would send it to 
F. If the velocity of projection were increased to a certain amount, 
he body would reach the antipodes at C, and even continue its 
course round the globe until it returned to the point A, whence 
t started. Were it not for the resistance of the air, a projected 
3ody, which now moves only three or four miles before fall- 
ng, would go nearly forty* miles ; and, could it be impelled with 
en times the velocity of a cannon ball, the centrifugal and centri- 
petal force would be in equilibrium, and, by their mutual action, 
:ause the body to revolve as a satellite around the earth. 




218. Explain Fig. 58. 



i 



PART II. 

OF THE MECHANICAL POWERS. 



LECTURE X. 

MACHINES. THE CORD. THE LEVEE. 

219. Science would be of little use to man, were it not capable 
of practical application. The subjects which we have consid- 
ered, viz : gravity, force and motion are, highly interesting as 
parts of a system of Philosophy, and because they explain many 
of the phenomena of nature. But we are not placed in this world 
merely to be amused, and that Philosophy which has no higher ob- 
ject would be scarcely worth the name. Knowledge is valuable, 
in proportion as it contributes to the comfort and happiness of man, 
or elevates and ennobles his soul. We have many wants, which 
can be supplied only by labor and industry ; such inventions, there- 
fore, as tend to facilitate labor, and give effect to industry, are of 
great value. We are indebted to science for most of those im- 
provements in the arts and manufactures, which give to the mod- 
erns such great advantages over the ancients ; not only in sup- 
plying necessary wants, but in greatly increasing facilities for the 
acquisition of knowledge, and in adding to the enjoyments and 
luxuries of life. 

220. The department of Natural Philosophy called Mechanics, 
exhibits the principles which are applied to the construction and 
operation of machines. The utility of machinery consists in the 
addition which it makes to the power of man. Under his control 
its practical results are, economy of time, and the application to 
valuable purposes, of many substances, which w T ould, otherwise, 
have been useless. 

219. Importance of the practical applications of science. 

220. Mechanics. Utility of machinery. 



70 NATURAL PHILOSOPHY. 

221. Man, besides human strength and the strength of other 
animals, has at his command the power of water, wind, and steam, 
with the force of springs and weights. Water acts by its weight, 
and the velocity which it acquires in falling. Wind acts by its 
volume or mass, and its velocity. Steam, which is the vapor of 
water produced by heat, has a tendency to expand itself, and its 
force is proportioned to the heat which generates it, and the pres- 
sure to which it is exposed. The strength of animals is com- 
monly made to act upon some center of inertia, by drawing, push- 
ing or pressing. 

222. There are three important circumstances to be considered 
in machinery ; 1st. the weight to be raised, or the resistance to 
be overcome ; 2d. the power by which this is to be effected ; and 
3d, the instruments employed. 

223. In machinery, it is necessary that motion should be pro- 
duced, and this motion properly applied. The instruments em- 
ployed for communicating motion, are called by various names. 
A tool is the most simple instrument, and is generally used by the 
hand ; as, a shoemaker's awl, a carpenter's saw. A machine is 
a complex tool, or a collection of tools, frequently put in ac- 
tion by inanimate force ; as a carding machine, which is moved 
by the force of running water. An engine is a powerful and com- 
plicated machine, as the steam engine. 

224. The ancients made little use of machines except in war, 
and in the erection of their stupendous works of architecture ; 
and these machines were chiefly moved by the strength of men and 
animals. In building the Pyramids of Egypt, it is said that 100,000 
men were employed for twenty years ; it is estimated, that, by the 
aid of modern machinery, one man could now, in the same time, 
perform the labor of 27,000 of the Egyptian workmen. 

225. Machines were first invented by men for the purpose of 
raising great weights, and overcoming great resistances. They 
do not produce power, but modify its effects ; that is, they increase 
or diminish the velocity of the moving power, change its direction, 
and accumulate momentum in order to exert it at one single effort ; 
or they distribute force among a great number of resistances, so 
dividing the force of resistance that it may be overcome by a series 
of actions, or by the continual action of the moving power. The 
term mechanical powers, is applied to a few simple machines, 

221. The forces under the control of man. How do these forces operate ? 

222. What circumstances are to be considered in machinery ? 

223. What is necessary in machinery ? Instruments employed for com- 
municating motion. 

224. Machines of the ancients. Advantages of modern machinery. 

225. Machines, why invented ? Do they produce power ? Why is the 
term mechanical Powers improperly applied ? 



MECHANICS. 71 

which are either used singly, or, are variously combined to form 
complex machines. But these machines are not, in reality, pow- 
ers, neither do they create power ; but aiding man so greatly in 
the adaptation of the powers of nature to his use, they have been 
regarded as the prime agents, when, in fact, they are only second- 
ary, and subservient to the existing powers of nature. 

22G. The simple mechanical powers are, the Cord, the Lever, 
and the Inclined Plane. 

The Cord. 

227. If a man wished to transport any weight, as a log of wood, 
without the assistance of the mechanical powers, he would first 
lift it with his hands, and then carry it in his arms. Here the 
muscular force of the man would be applied merely to overcome 
gravity, and would, consequently, act in a vertical direction. Were 
a cord to be tied to the log, and the strength of the man exerted in 
pulling, the direction of the force would then be horizontal. The 
cord w r ould serve to change the direction of the force. The manner 
in which this force is modified is thus ; instead of overcoming the 
weight of the log, or gravity, it only overcomes friction, which, 
though proportional to the weight of a body, is not equal to it. 

The Lever. 

228. The lever is a rod or bar, which is used in raising a weight, 
or overcoming a resistance by being placed on a fulcrum or prop ; 
which point is the center of motion. The name lever was given, 
because this mechanical power was first applied only to the rais- 
ing or lifting of weights. The center of motion is the fulcrum. 

The force which gives motion, is 
Fig. 59. called the power, that which re- 

sists it is called the weight, or 
resistance ; a is the part of the 
lever at which the power, or the 
strength of a man's hand, is ap- 
plied ; f is the fidcrum ; and b the 
weight. 

229. The lever changes the direction of forces into opposition ; 
that is, when the power descends, the resistance ascends, viz., as 
the man's force presses down the lever, the weight rises. 

The beam of a common balance is a lever with equal arms; 

226. What are the simple mechanical powers ? 

227. Use of the cord. 

228. What is the lever? Explain the terms, fulcrum, power, and weight. 

229. How does the lever change the direction of the forces ? How 
may a common balance be regarded as a lever? Effect of placing the 
fulcrum nearer the weight. How may a bar connecting unequal weights 
be put in equilibrium ? 




72 



NATURAL PHILOSOPHY. 



Fig. 60. 




the pointy*, by which it is sup- 
ported is the fulcrum. When the 
scales are empty, or when they 
contain equal weights, they are 
in equilibrium; the center of 
gravity, which is then in the 
middle of the beam, being sup- 
ported by the fulcrum f. If 
one scale contains a greater 
weight than the other, the cen- 
ter of gravity is not in the mid- 
dle of the rod, but nearer the 
greatest weight, which descends because it outweighs the mass 
in the other scale. Now if the fulcrum be removed and placed 
nearer the greater weight, the scales may be made again to balance 
each other ; from whence it appears, that the nearer the weight is 
to the fulcrum, the more its resistance is diminished. 

If the ball A weigh- 
Fig. 61. ing three pounds, and B 

A weighing one pound, be 

fixed to the opposite ends 
of an iron bar, the bar 
will be in equilibrium if 
supported at the point c, 
three times as far from 
the lighter ball as from the heavier one. We may consider the bar 
as a lever, the large ball as the resistance or force to be over- 
come, and the supporting point as the fulcrum. 

230. It is a fact well understood by children in amusing them- 
selves by balancing upon a board placed across a prop, that when 

their weights are not equal, the 




Fig. 62. 




heaviest shall be nearest the 
fulcrum, or center of motion. 
Now the child at A, moves with 
greater velocity than the one at 
B, because the former, in rising 
and falling, describes the arc 
of a larger circle, the two parts 
of the lever being considered 
the radii of two circles. If A D, 
represent the arm of the lever 



230. How does the lighter child balance the heavier one in the see- 
saw. Effect of velocity. The length of the lever should be proportion- 
ate to the weight to be raised. How might a number of children at 
either side of the fulcrum balance each other? 



THE LEVER. 73 

supporting the lesser weight, this will be a radius of a larger circle ; 
and B D, on which the greater weight moves, will be the radius 
of a smaller one ; A C being an arc of the larger, and B C, an 
arc of the smaller circle. 

Thus we see that by means of the lever, properly adjusted, the 
lighter child balances the heavier one ; and because the lighter 
weight, in rising and falling, describes in the same time the arc of 
8 greater circle than the heavier weight, the former moves with 
greater velocity ; velocity here being equivalent to weight. Great 
weights may be raised with long armed levers, since the longer 
the arm to which the power is applied, the greater is the effect 
produced by it ; because the velocity of the power is thus rendered 
proportionally greater than that of the weight. In the example 
of the children and the balancing board, the heavier child is to be 
considered as the weight, or resistance, and the lighter child the 
power. 

A number of children might be placed at either side of the ful- 
crum provided that the sum of the weights of all on one side, mul- 
tiplied by their respective distances from the fulcrum, were equal 
to the sum of the weights of those on the other side multiplied by 
their distances, respectively, from the same point. If a plank be 
twelve feet long, and the fulcrum be placed four feet from the end 
B, (see Fig. 62,) a child weighing 30 pounds at the end A, would 
support two children weighing 40 pounds each, one being placed at 
B, and the other two feet nearer the fulcrum. This will appear from 
calculation, for the weight of the child at A, 30 X 8, his distance from 
the fulcrum, gives for the product 240 ; and the weight of one child, 
40 X 4= 160, and another at two feet from the fulcrum, 40 x 2= 80, 
will by the addition of the products make 240. The plank being 
thus brought to a state of equilibrium must in order, to make it 
vibrate, have some impulse given to it by some motion of the 
children, or by their alternately pressing their feet against the 
ground. 



LECTURE XL 



THE LEVER. 



231. Levers are of three kinds, according to the position of the 
power and weight with respect to the fulcrum. In the first kind 



231. Different kinds of levers. 



74 NATURAL PHILOSOPHY. 

of lever, the fulcrum is between the power and the weight ; in the 
second kind, the weight is between the power and fulcrum ; in the 
third kind, the power is between the weight and fulcrum. 

Levers of the first hind. 

232. In a lever of the first kind, the fulcrum, F, is between tJw 
power, P, and the resistance or weight, R. A poker used for rais- 
ing coals in a grate, is an example, the bar 

Fig. 63. of the grate being the fulcrum. The com- 

mon balance is also a lever of the first 
■ * I kind. But where the fulcrum is equally 

i v J*, distant from the two forces, as in the bal- 

ii «^\ ance> there is no mechanical power, for as 

the two arms of the lever are equal, no- 
thing is gained by velocity. False balances have the arms of the 
lever unequal in length. Thus a dishonest trader defrauds, both 
in buying and selling. In selling, he puts his goods in the scale, 
which is suspended to the longer arm, and here they appear to 
weigh more than they do in reality, by balancing a greater weight 
nearer the fulcrum. In buying, he puts the article of merchan- 
dize into the scale suspended to the snorter arm, or nearer to the 
fulcrum, where the real weight of the commodity would be bal- 
anced by a lighter weight in the other scale. The fraud may be 
detected by making the weights and merchandize change places. 
A weight of one pound will balance another of three pounds, if the 
smaller weight be three times farther from the fulcrum than the 
larger one. 

233. If it be required to raise a stone, s, (at A) which weighs 
1000 pounds, by the strength of a man equal to 100 pounds weight, 

Fig. 64. 




a lever, a c, which rests on the prop b, should be placed with one 
end under the stone. As the man's strength is only equal to the 
tenth part of the weight of the stone, the arm o the lever, b a, 
must be ten times as long as the arm b c, in order that the power 

232. Lever of the first kind. False balances how contrived. 

233. To move a weight of 1000 pounds by a force of 100 pounds. 



THE LEVER. 



75 



Fig. G5. 



§ 



and weight may balance each other. In another case illustra- 
ting the same principle, the hand represents the force, raising the 
heavy weight B, by a lever resting upon the fulcrum E. 

234. The steel-yard is a lever of the first 
kind, having its arms unequal ; and any 
weight, as b on the long arm, will balance 
•=i*r ^ as much more weight than a on the short 

^|p^~nTizx^-L^Ljr=> arm, as b is farther from the fulcrum than a. 
Thus if the hook at the short end, be one 
inch from the fulcrum f, a pound weight b, 
I ]j|" will balance four pounds, a, at the short arm. 

If the article to be weighed be heavier than b, or more than one 
pound, it must be removed farther from the fulcrum in order to find 
its equipoise against the weight a: if lighter than b, or less than 
one pound, it must be nearer the fulcrum. The figures on the 
long arm of the steel-yard represent pounds, the divisions between 
them half pounds. Steel-yards are usually marked by notches sig- 
nifying halves and quarters of a pound ; and sometimes by notches 
representing ounces. A steel-yard has usually two graduated 
sides, one for smaller, the other for greater weights. On the side 
for the greater weight, the weight is placed nearer the fulcrum. 

The bent lever balance is repre- 
sented in the figure. The weight C 
acts as upon the point D ; and the 
weight in the scale acts at K ; hence 
an equilibrium will take place, when 
the article weighed bears to C the 
same ratio as D B to B K. Now 
every increase of weight added to 
the scales causes C to rise on the arc 
F G, and D to recede from B. Hence 
the different positions of C, according as 
different weights are added to the scale, 
may be easily determined, and the cor- 
responding numbers marked on the 
scale F G.* 

235. A pair of scissors is composed of two levers acting con- 
trary to each other, being held together by a rivet, which is the 
common fulcrum for both levers. In using them, the hand is the 




Olmsted. 



234. The steel-yard. How can a pound weight be made to balance four 
pounds ? If the weight be greater or less than four pounds. The bent lever 
balance. 

235. Other examples of levers of the first kind. 




76 NATURAL PHILOSOPHY. 

power, and the article cut, is the resistance. The handles are 
usually nearest the fulcrum, and are then the short arms of the 
lever. Materials which are hard to cut, are best operated upon 
by being placed near the rivet, or fulcrum. In shears used by tin- 
ners in clipping tin, the handles are very long, thus giving an in- 
crease of power, by bringing the resistance near the fulcrum. 
Pincers and sugar cutters are also double levers of the first kind. 

236. Figure 67 shows 

Fig. 67. a long, single lever turn- 

B ing on a strong iron-pin 

as a fulcrum; the long 
arm gives a great advan- 
tage in raising heavy bod- 
ies, as by means of it, a 
small power acting at A, 
may overcome a great resistance at B. An ancient philosopher, 
Archimedes, said, " Give me a lever long enough and a fulcrum 
strong enough, and with my own weight I will lift the world. But 
as a power acting by a lever produces a force, greater in propor- 
tion as the distance from the fulcrum is greater, because of the 
greater velocity thus acquired ; it follows from mathematical de- 
monstration, the power being compared with the resistance, that 
the philosopher, if he had been furnished with the long lever and 
strong fulcrum which he desired, must have moved with the velo- 
city of a cannon ball for millions of years, in order to have raised 
the earth the smallest part of an inch. This may be illustrated by 
a common example, that of prying a nail by means of what is 
called a claw-hammer, which is a bent lever. Let the handle or 
shaft of the hammer, be six times as long as the iron part that 
draws the nail, and which rests against the board, a man will pry 
up the nail with one sixth part of the power that he must use to 
pull it out of the board with a pair of pincers. In the latter case, 
the nail would move as fast as the hand, but in the former case, 
the hand would move over six times as much space as the nail, by 
the time the nail is drawn out. That is, the hand moves six inches, 
in moving the nail one inch. 

Levers of the second kind. 

237. In a lever of the second kind, the weight is between the ful- 
crum and the power ; in this case, the forces are on the same side ; 



236. Advantage of a long lever. Assertion of Archimedes. Velocity ne- 
cessary for a man to move the earth with a lever. Illustration. 

237. Levers of the second kind. Example. Advantage gained by this 
lever. Why is this the most efficient kind of lever 7 






THE LEVER. 



77 




site 



Fig. 69. 




the more distant force acts as the power, and 
the nearer, as the weight or resistance. In 
Fig. 69, a hand-spike is represented as a lever 
of the second kind ; the ground F, is the ful- 
crum, the barrel or the weight W, is next, 
and the hand or power, at the end oppo- 
the fulcrum. The power, as in levers 
of the first kind, is at a greater dis- 
tance from the fulcrum than is the 
weight, and the advantage gained by 
this lever, is also greater, in propor- 
tion as the distance of the power 
from the fulcrum, exceeds the distance 
of the weight from the fulcrum. Thus, 
if P be five times as far from W as is 
F, then one pound at P will raise six 
pounds at W. 

This is the most efficient kind of lever. The effect produced in the use 
of levers depends, in part, upon this, whether the power and weight move in 
contrary directions, or in one and the same direction. In the use of the lever 
of the first kind, the power moves in one direction, while the weight moves in 
another ; hut in the use of the lever of the second kind, hoth the power and 
the weight move in one ami the same direction. P is equal to 1 pound?, and 
F is equal to 5 pounds; the barrel is therefore moved by a force of 6 
pounds. ]f we conceive Fig. 69, to represent a lever of the first kind ; then 
W becomes the fulcrum, and P becomes a pulling instead of a pushing 
power, and the weight would be moved at F. Now 1 pound at P would 
create a pressure upward of 5 pounds at F, aud a pressure downward of 6 
pounds on the fulcrum W. 

238. Two persons car- 
Fig. 70. lying & burden upon a 
pole, bear shares of the 
load, in the inverse propor- 
tion of their distances from 
it ; that is, the one who 
is nearer to it, bears the 
greater share ; if A be four 
times as near the load as 
B, then A will bear four 
times as much of the weight 
as B. 

239. A door moving on its hinges is a lever of the second kind. The hinges 
are the fulcrum or center of motion, the door is the weight or resistance, and 
the hand, in opening and shutting, is the power. Let a person attempt to 
push open a large heavy door by using his strength near the hinges or ful- 




238. Other examples of levers of this kind, 
weight. 

239. A door, a lever, &c. 

7* 



Two persons carrying a 



78 



NATURAL PHILOSOPHY. 



crum, and he will find much force necessary; whereas, by pushing at the 
part farthest from the hinges, he will move the door with ease. If, while a 
person is sitting upon a bench near the middle, another should attempt to 
raise the bench, by one end, the resistance would be much greater than if the 
person were sitting at the opposite end. 

The oar of a boat, is also a lever of the second kind ; the water being the 
fulcrum, the boat the resistance, and the hand of the rower, the power. The 
mast of a vessel, may also serve as an example of a lever, the bottom of a ves- 
sel being the fulcrum, the vessel the weight, and the wind the moving power. 

The crane, a lever of the second kind, is used for transporting great weights 
a short distance, as heavy boxes of merchandize from a vessel to the wharf. 
An example of the crane is seen on a small scale in the apparatus of a kitchen 
fire place. 



Levers of the third kind. 



Fig. 71. 




240. In levers of the third hind, the forces, 
as in those of the second hind, are on the same 
side, but the power is applied between the 
weight and the fulcrum. In a lever of this 
kind, the power being nearer to the fulcrum 
than the weight is, the advantage is in favor 
of the latter ; and a greater power would be 
required to move the weight by means of this lever, than without 
its aid. But in this case the power will raise the weight through 
a greater space than that through which the power itself passes, 
thus giving increased velocity to the weight. This kind of lever 
is not used to overcome great resistance, but to move a weight 
with greater speed, or on account of its adaptation to some par- 
ticular purposes. 

241. In elevating a ladder,the ladder is first a lever of the second, 
and afterwards of the third kind. While the center of gravity is be- 
tween the hands that raise it and the ends on 
Fig. 72. which it rests, the ladder is a lever of the sec- 

ond kind, but when the hands pass the center 
of gravity, (as is seen in the figure,) the lad- 
der becomes a lever of the third kind. Here 
the longer part of the ladder, or the resist- 
ance, has the same advantage in velocity, which is possessed 
by the power acting at the long arm of a lever of the first kind. 
The nearer to the ground or fulcrum of the ladder, the power 
of the hand is applied, the greater the difficulty in raising the 
weight. The shears used for shearing sheep, are double levers 
of the third kind ; the parts are not connected by a rivet, which 
forms the fulcrum in common shears, but the power of the hand 
acts by pressure on a part near the middle ; the fulcrum, or sup- 



240. Levers of the third kind. 

241. Examples of levers of the third kind. 




THE LEVER. 79 

port, being at the end opposite to that in which is the resistance, 
or the wool to be sheared. The advantage of these shears is, that 
ltttle force is needed ; what the power loses, is gained in the ve- 
locity with which the parts next to the resistance act. In using 
the common jire tongs, the ends of the tongs move with much 
greater velocity than the fingers, and it is only a small weight that 
we can lift with them, and this weight is less in proportion, as the 
legs of the tongs are long. 

242. The most interesting examples of levers of the third class are 
to be found in the bones of animals, which give rapidity of motion 

at the expense of power. Here the 
Fig. 73. bone may be considered the lever, the 

joint the fulcrum, and the muscles 
the power. In the human arm, the 
elbow d, is the center of motion, or 
fulcrum ; at e, is the muscle, which 
acts as the power in raising a weight, 
a ; the muscle being about one tenth 
part as far below the elbow as the 
hand, it follows that it must exert a power equal to one hundred 
pounds to raise a weight of ten pounds. By this we see how 
strong must be the muscles which give power to the animal frame ; 
but this strength seems necessary in the position the muscles oc- 
cupy, acting, as they do, at the mechanical disadvantage of being 
so near the fulcrnm. But by this loss of power, much is gained 
in velocity ; and to man, with all his advantages of various me- 
chanical powers for increasing force, it is of great importance that 
his hands are so supported, that he can move them with quickness, 
and adapt them readily to a great variety of motions, impelling 
other forces at his will, and causing them to obey his bidding. 

Compound Levers. 

243. Any number of levers maybe connected together, so as to constitute 
a system of levers, the power acting on the end of the first lever raising the 
end of the second, and that depressing the end of the third so as to raise the 
weight at the opposite extremity. In this machine, the force is inci-eased in 
proportion to the number of levers employed. Ex. In a compound lever, the 
lengths of the longer arms are 5, 10, 16 feet, respectively, and of the shorter, 
1, 2, 3 feet: what power applied to the longer side, will be required to bal- 
ance a weight of 100 pounds ? 

5X10X16 : 1X2X3 : : 100 : performing the multiplication indicated, the pro- 
portion becomes 800 : 6 : : 100 : multiplying the mean terms of this propor- 
tion and dividing by the extreme, we have 100X6=:600-=-800, but as we 

242. Bones of animals examples of levers of the third kind. The human 
arm. 

243. Compound levers. 



80 NATURAL PHILOSOPHY. 

cannot divide a less number by a greater, we express it in the fractional 
form -fg-g-; reducing this fraction to its lowest terms, it equals f the last 
term, therefore we have lbs. lb. 

5X10X16 : 1X2X3 : : 100 : f Ans. 



LECTURE XII. 

THE INCLINED PLANE. 

244. The inclined plane is the most simple of the mechanical 
powers. It is used in raising heavy weights. A plank placed in 

a slanting position for the purpose of rolling up 
Fig. 74. casks into a warehouse, is an example ; a c, re- 
presents an inclined plane, a b, its height, b c, 
its base. That a weight could be more easily 
rolled up a slope, than raised perpendicularly, is 
very evident. But the advantage is gained at the 
expense of time, because instead of moving directly from b to a, 
the weight moves over the line a c ; the resistance being less in 
proportion as the line a c is longer than the line a b ; therefore, 
as the length of the plane is to its height, so is the resistance di- 
minished. In the inclined plane, the power has to overcome only 
a portion of gravity at a time, and this portion is greater or les-, 
as the plane is more or less elevated. 

245. On a plane, perfectly horizontal, as at A, (Fig. 75,) the pres- 
sure of a body is entirely sustained by the plane, and the pressure upon 

Fig. 75. 





it is equal to the whole force of gravity. When one end of the plane 
is elevated, as at B, the force of gravity is resolved into two forces, 
the one acting parallel to the plane, and the other acting perpen- 

244. Inclined plane. Advantage gained at the expense of time. By what 
rule is the advantage of the inclined plaue estimated ? 

245. In what case is the pressure on a plane equal to the whole force of 
gravity? What is the effect of inclining this plane in respect to gravity? 
Of raising the plane perpendicularly ? 




INCLINED PLANE. 81 

dicular to it. In proportion as the plane is more elevated, that 
part of the force of gravity which acts in a line with it is increased ; 
and when the plane is raised perpendicularly as at C, the whole 
force of gravity acting in one direction, causes the body to offer 
an undivided resistance to the power which should attempt to sup- 
port it. 

24G. The power applied in raising a weight upon an inclined 
plane, must be to the weight, as the height of the plane is to its length. 
Suppose the perpendicular height A B, 
to be one foot, and the inclined sur- 
face A C to he four feet; then a weight 
W, of four pounds, resting on the plane, 
icill balance one pound P, acting over 
a pulley ; that is, one fourth of the 
weight necessary to lift a weight through the space A B, the ver- 
tical height, would be sufficient to force it up the inclined plane, 
from C to A. Here it will be seen, that what is gained by power 
is lost in time, which is the case with all kinds of machines. 
From the simple nature of the inclined plane, it is probable that it 
was used in remote periods of antiquity. The Egyptians are sup- 
posed to have made use of very long inclined planes in elevating 
the huge masses of stone which form the pyramids. 

247. Roads over declivities are inclined planes. A horse in draw- 
ing a load over level ground, meets with no resistance from gravity ; 
he drags but does not lift the weight, that is, the resistance is from 
friction, which being proportioned to weight, is of course greater 
with a heavy than with a light load. But in drawing the load up 
a hill, the horse has to overcome more or less of the force of 
gravity ; that is, he lifts a part of the load, and this part is greater, 
in proportion to the steepness of the ascent ; or, in other words, he 
lifts such a part of the weight, as bears to the whole weight, the 
proportion, that the perpendicular height of the hill bears to its 
length. If, in a length of ten feet, there is a rise of one foot, the 
horse lifts a tenth of the load. In constructing roads, there has 
been, in our country, a great disregard of mechanical principles. 
The desire of " going straight ahead," has led road- surveyors to 
go up and down hills, when, by going round their bases, they 
would have an equal distance over a level road. Railroads are 
constructed on the principle of the inclined plane. They are made 
either level, or with so gradual a slope, that the drawing horse, 

246. Rule with respect to the power needed to raise a weight on an in- 
clined plane. Examples. 

247. Roads. What is to be overcome in drawing a load on level ground? 
What in drawing a load up hill ? Should roads be made to go over, or around 
a hill ? 



82 NATURAL PHILOSOPHY. 

or steam engine, has little more than the friction of the carriage 
to overcome. By means of railroads, the hills and valleys of an 
uneven country are reduced to horizontal and inclined planes. In 
passing considerable elevations, it is, sometimes necessary that 
the inclined planes should be very steep ; in which case, cars are 
drawn up by means of a steam engine stationed on the summit ; 
and sometimes cars descending on one side, are made to draw 
up others on the other side, the two being connected by a rope 
passing round a pulley on the summit. 

248. Bodies descending freely down inclined planes move with 
uniformly accelerated velocity, but this velocity is not so great 
as in falling through an equal space in a perpendicular direction. 

Thus, supposing the distance from A to B, 
to be equal to that from A to C, and the for- 
mer an inclined plane, the latter perpendic- 
ular ; a ball falling from A to C, would ac- 
quire greater velocity, than in rolling down 
the inclined plane to B ; but let the ball move 
from A to D at the base of the plane, and 
its velocity will be equal to that gained by 
falling from A to C. Rule — the velocity ac- 
quired in falling from an inclined plane is equal to that acquired 
in falling through the perpendicular height of the same plane. 

Compound Mechanical Powers. 

249. The three mechanical powers, viz., the cord, lever, and 
inclined plane, appear under the different modifications of the 
wheel and axle, the pulley, the wedge, and the screw. The wheel 
and axle is a variety of the lever, both machines being regulated 
by the same principle. The pulley depends for its utility upon 
the cord, though as it is used with wheels, it partakes of the na- 
ture of the lever. The wedge is a double inclined plane, acting 
on the same principle as the single inclined plane, but with twice 
the effect. The screw, which is a modification of the inclined 
plane, operates through the aid of the lever. 

248. Velocity of bodies moving freely down an inclined plane. Rule. 

249. Different modifications of the mechanical powers. 




THE PULLEY. 



LECTURE XIII. 



THE PULLEY. 



Fig. 78. 




250. The cord is the essential part of the pulley, but it cannot 
be used to advantage without a wheel. If a rope were perfectly 
flexible, it might be bent over any sharp edge, and thus enable 
force to overcome resistance, or to communicate motion in any 
desired direction. 

251. Suppose P to be a sharp edge, with a rope passing over 
it ; a sufficient force F, acting in the direction F P, would over- 
come the resistance R, and produce motion 
in the line R P. But as no materials of 
which ropes are made, can be perfectly flexi- 
ble, and as they are rigid in proportion to 
their strength or ability to transmit force ; 
cords could not be applied to machinery, 
except some means had been devised to 
overcome these obstacles. If a cord were 
to be used to transmit a force from one di- 
rection to another, it would require some 

force to bend it over the angle P, and this by its sharpness, would 
soon break the cord. 

252. By bending a cord over the surface of 
a curve, it may be made to sustain a certain 
weight, but when motion is to be produced, the 
rope in passing over the curve would meet with 
much resistance from friction. But in the pulley, 
the curved surface moves with the rope, and 
thus is obviated the difficulty which, otherwise, 
would attend the use of this mechanical power. 

253. The wheel of the pulley is called a 
sheave ; this is fixed in a block and turns upon 
a pivot. In the edge of the wheel is a groove, 
made for the rope to move in ; the wheel itself 
revolves on the pivot, which is its axis of mo- 
tion. The figure represents what is called a 

fixed pulley. 
254. The fixed pulley gives no mechanical advantage, but its 




250. Essential part of the pulley. 

251. Cord passing over an edge or angle. 

252. Curved surface of the pulley. 

253. Wheel or sheave of the pulley. 

254. Use of the fixed pulley. 



84 



NATURAL PHILOSOPHY. 



Fig. 80. 



chief use is to change the direction of forces. This, however, 
renders it of great importance, since in the application of power, 
whether of mentor animals, there are always some directions 
which are more convenient and advantageous than others. A 
machine, therefore, which gives man the ability thus to transmit 
or change the direction of moving powers, is not less important 
than one which enables him with the aid of a small power to 
overcome a great weight. 

255. It would be very inconvenient to climb up, in order to roll 
a curtain ; but by means of the pulley, the object is effected by the 
mere drawing down of a cord. It is also much easier to raise a 
bucket from a well, by means of drawing downwards upon a rope 
fixed to a pulley, than to lift the weight 
by pulling it upwards. Boxes, bales of 
goods, and casks, are raised, by pulleys, to 
the upper lofts of stores, and huge masses 
of stone, to the fourth and fifth stories of 
buildings. By means of the pulley which 
is used in hoisting sails and weighing 
heavy anchors, a smaller number of sea- 
men than would otherwise be required, 
are enabled to manage a ship. 

256. The better to adapt the power to 
the resistance, two pulleys are often used. 
The strength of a horse may be so direct- 
ed as to carry heavy loads to great per- 
pendicular heights. Thus suppose B and C two fixed pulleys, 
and A, a block of marble fastened to a rope, which being 
carried over the pulley B, passes round C, and in the 
horizontal direction thus given, is drawn by the horse 
to which it is fastened. Every step of the animal causes 
an ascent of the stone, until arriving at the pulley B, 
it is applied to its destined use by the workmen at 
the top of the building. 

257. By means of the fixed pulley fastened near the 
window of an upper story, a man might let himself 
down, to escape from fire, when other means were 
wanting ; and, by the same means, a person might draw 
himself up from a well or mine. But an attempt of this 
kind would be dangerous, except in the case of one hav- 
ing great muscular strength in proportion to his weight. 





255. Applications of-the pulley. 

256. Why are fwo pulleys sometimes used ? 

257. Descending and ascending by means of a fixed pulley, 
increase of power gained by the fixed pulley ? 



Is there any 



THE PULLEY, 



85 



Fiji. 82. 



258. The movable pulley gives to the power a double advan- 
tage over (he weight. B represents a movable pulley, in connec- 
tion with a fixed pulley C. The weight W, is attach- 
ed to the movable pulley, and as it bears equally upon 
the two parts of the rope which pass round the pulley 
15, the power P having only to resist the force B C, 
has to sustain but half the weight in order to balance 
W. Therefore, when the power is equal to half the 
weight, an equilibrium is maintained. If the weight is 
12 pounds, it will be balanced by a power equal to 

JjL pounds ; but for every inch that the weight is raised, 
Hl w ' the rope must be drawn at P two inches. With the 
movable pulley, a man raises twelve pounds with the exertion of 
only so much strength, as would, otherwise, be required to raise six 
poun Is : but, in order to do this, his hands move through a space 
of tw> feet, whereas, if he lifted the whole weight, they would only 
move through a space of one foot. Thus the advantage gained, is 
in proportion to the space passed through. It is, as if the weight 
were divided into two equal parts, and raised successively. In the 
novable pulley, as in the lever, the deficiency in the power is com- 
ensated by greater velocity. 

259. Compound pulleys are combinations of many pulleys, in 
which the weight is distributed over a greater number of parts 

of the rope, each part, consequently, sus- 
taining a smaller portion of the weight. 
As the hands move over twice the space 
for every pulley, it follows that two 
acting pulleys, increase the power four 
times, three acting pulleys, six times, 
&c. 

260. Fig. 83 represents a system of 
pulleys called a tackle, having the rope 
successively passed over the pulleys above 
and below, until after passing over the 
fixed pulley A, it is attached to the power. 
The weight is as many times greater than 
the power, as is the number of the folds 
of cord. Fig. 84 represents a tackle hav- 
ing the pulleys arranged side by side, in 
two blocks placed, the one above another. 
In the upper block there is an addition- 



Fig. 83. Fig. 84. 




•258. Advantage of the movable pulley. 
259. Compound pulleys. 

SCO. How may a weight of 72 pounds be held in equilibrium by a power 
of 9 pounds ? 



86 NATURAL PHILOSOPHY. 

al wheel or pulley, which adds 1 to the power of the ma- 
chine. 

By means of four movable pulleys, a weight of 72 pounds 
may be held in equilibrium by a power of 9 pounds ; dividing 
the weight by 8 the folds of cord, we have the quotient, 9. But 
the power, when in motion, must pass over eight times as much 
space as the weight ; therefore what is gained in power is lost 
in time. 

261. Owing to the friction of the wheels and blocks and the 
stiffness of ropes, all the advantage which in theory is stated as 
being gained from the use of blocks of pulleys, is not realized. 
The weight of the several parts in the machinery is also to 
be considered, in estimating the advantage of this mechanical 
power. 



LECTURE XIV. 



THE WHEEL AND AXLE. THE WEDGE. THE SCREW. 



262. The wheel and axle, is a wheel turning round, together 
with its axis. — The power is applied to the circumference of the 

wheel, and the weight to that of the axis, by 
Fig. 85. means of cords. Let A B represent an axle, 

turning upon pivots at its extremities, and 
having a rope coiled around it, which sustains 
the weight W. Around the wheel C, which 
is fixed to the axle, a rope is coiled in a con- 
trary direction from that around the axle, and 
supports the power P. In turning together, 
the wheel will take up, or throw' off, as much 
more rope than the axle, as its circumference 
is greater than that of the axle. If the pro- 
portions be as 6 to 1, one pound at P will balance six pounds 
at W. 

263. The wheel and axle is considered as a lever of the first 



261. Effects of friction, and of the stiffness of ropes. 

262. How is the power applied to the wheel and axle ? 

263. Describe the operation of the wheel and axle. 




WHEEL AND AXLE. 



87 




Fig. 86. kind, in which c, the center of the axle, repre- 

sents the fulcrum ; the radius of the wheel the 
longer arm of the lever ; and the radius of the 
axle the shorter arm. Therefore, the power 
and weight are in equilibrium, when the power 
bears the same proportion to the weight, as 
the radius of the axle c o, bears to the radius 
of the wheel a o. Thus if the diameter of the 
wheel is ten times that of the axle, a power 
of one pound will balance a weight of ten 
pounds. 

264. Since the wheel and axle are shown to be of the same 
nature as the lever, the inquiry may naturally arise, " wherein 
consists the advantage of the former over the latter ?" When a 
lever is used for raising a weight, it can act but through a small 
space at a time ; but, from its simplicity, the lever is of great use 
in raising heavy weights through a short space. When a contin- 
uous motion is to be produced, as in drawing water from a well, 
raising ore from a mine, &c, some contrivance is necessary to 
render the action of the lever continuous ; the spokes or radii of 
the wheel and axle acting as so many levers, and revolving regu- 
larly and without intermission, produce this desired effect. 

265. Although the axle is usually nothing but a cylinder fixed 
upon pivots, yet, as it revolves about these as a center of mo- 
tion, it is, in effect, a wheel ; and half its diameter or one of its 
radii, bears the same proportion to the whole circumference 
of the axle, as a spoke of a wheel to the circumference of the 
wheel. 

266. In the common windlass, used in drawing water, what is 

called the crank or winch B 



Fig. 87. 



C, serves the same purpose 
as a w r heel, being the radius 
or half the circumference ; 
D is the handle by which the 
power is applied. At each 
revolution of the crank, a 
circle is described ; and the 
effect of the revolution upon 
the axle is the same as if the 
wheel were entire. There- 
fore it follows, that as B C 
represents the spoke of a 



264. Wheel and axle considered as a lever. Rule. Advantage of the 
wheel and axle compared with that of the lever. 

265. How may the axle be considered a wheel ? 

266. Describe the common windlass. 



88 



NATURAL PHILOSOPHY. 



Fig. 88. 




wheel, or the radius of a circle, the power will be increased, in 
proportion as the circle described by B C, is larger than the cir- 
cumference of the axle, A E. 

267. The capstan used in ships and dock-yards, for weighing 
heavy anchors or drawing vessels into 
harbor, is one of the most useful applica- 
tions of the wheel and axle. In this, tho 
axle is vertical ; its circumference, near 
the top, is pierced with holes, into which, 
when the machine is to be worked, are 
inserted long levers, called capstan bars. 
These answer the same purpose as the 
spokes of a wheel, or the crank of a 
windlass. The men who work the cap- 
stan walk around the axle, pressing the 
bars forward, and the cable is thus wound about the axle with a 
force sufficient to lift a heavy anchor, or draw a large ship into 
harbor. 

268. The treadmill, is turned by 
Fig. 89. the weight of men, who step for- 

ward as fast as the wheel descends, 
thus maintaining their position at 
the extremity of the horizontal di- 
ameter of the wheel. Horses may 
be made to work the machinery of 
a mill, when harnessed to the ex- 
tremities of shafts or long levers 
fixed to an axle, which they turn by 
walking in a circle ; examples of this may be seen in cider-mills, 
brick-yards, &c. The horse-boats used in crossing ferries, are 
moved by the stepping of the animal upon a horizontal wheel con- 
nected with paddles, or, with a perpendicular wheel. 




Compound Wheel and Axle. 

269. In the compound wheel and axle, the power is to the weight, 
as the product of the diameters of all the smaller wheels, is to the 
product of the diameters of all the larger wheels. Thus the power 
being applied to the winch P Q, acts upon the small wheel A, 
which acts upon the large wheel B, this upon C, and this again 
upon D, which exerts its original and accumulated power upon 



267. What is a capstan ? 

263. Tread-mill. Mills and boats moved by horses. 

269. Relations of the power and weight in the compound wheel and axle. 
Rule to be applied to the action of the compound wheel and axle. 



WIIKKL AND AXLE. 



89 




Fig. 91. 



1, 




Fig. 90. the axle E, which supports the weight W. 

Now, if the diameters of the three smaller 
wheels, including that of the axle, be seve- 
rally, one fourth those of the larger wheels, 
(of which the diameter of the wheel de- 
scribed by the winch P Q, that is twice P 
Q, must be considered as one) then the 
power will be to the weight as lXlXl • 
4X4X4, that is as 1 to 64 ; and a force 
often pounds applied at P, will balance a 
weight of 640 pounds applied at W ; or in 
other words, if one pound will balance 64 
pounds, ten pounds will balance 640. 

270. " It is, sometimes, desirable to make a variable power pro- 
duce a constant force. This may be done by making its velocity 

increase, as its intensity diminishes. 
We have an example of this in the 
reciprocal action between the main- 
spring and fusee of a watch. The 
main-spring is coiled up in a box A, 
and is connected with the fusee B, 
by a chain. When the watch is first 
wound up, the spring acts with its greatest intensity, but then as 
the wheel B turns, it uncoils with the least velocity ; but on ac- 
count of the varying diameters of the wheels of the fusee, the ve- 
locity is continually increased, as the intensity of the spring is 
diminished."* 

One turn of the axle on which the watch key acts, is, by the 
train of wheels attached to it, rendered equivalent to about four 
hundred beats of the balance wheel, and thus the exertion during 
a few seconds, of the hand, in winding up a watch, produces mo- 
tion for twenty-four hours, or more. 

271. Wheels may be connected by bands, as in the turning- 
lathe, and the common spinning-wheel. A spinning-wheel, as A 

of thirty inches in circumference, turns, by 
its band, a spindle of half an inch, 6, sixty 
times, for everyturn of itself. If the wheels 
connected by bands are required to revolve 
in the same direction, the bands are ar- 
ranged as at A ; but if they are required to 
revolve in different directions, they are ar- 
ranged as at B, where the hand is crossed. 

* Olmsted. 



Fig. 92. 




270. Constant force produced by a variable power. Example. 

271. Wheels connected by bands. Cross-band. 

8* 



90 



NATUKAL PHILOSOPHY. 



In spinning, the band of the wheel is fixed as at A ; but in twist- 
ing two or more threads together, the band of the wheel is crossed 
as at B. Two persons standing opposite and facing each other, 
in twisting a string, the fingers of each having the same motion, 
will produce a twist like that made with the cross-banded wheel. 



The Wedge. 



Fig. 93. 




272. The wedge may be considered as two inclined planes, whose 
bases are joined. The wedge is forced in between resistances to 

separate them, instead of having the re- 
sistance moved over its surface as in the 
inclined plane. The more acute the 
angle A, at the extremity of the wedge, 
the greater its power is estimated to be. 
But the wedge is used in such a manner 
that, it is difficult to compute its actual 
power, as this must depend greatly on 
the strength of the blow with which it is forced against a resist- 
ance. 

In splitting logs of wood, and masses of stone, this mechanical 
power possesses a peculiar advantage, for, by its means, a great 
force can be exerted through a small space. 

273. A wedge is of that form, known in geometry, as a trian- 
Suppose the edge, or angle E F, impelled against 
a block of wood, by a force applied at the surface, 
A B D C, the effect of this force will be in the 
ratio of the line D F, to the line G D, or, as the 
sides of the wedge are, to half its breadth. That 
is, the power is increased, either by diminishing 
the back of the wedge, or by increasing its length. 
Sharp edged, and sharp pointed instruments act on 
the same principle as the wedge ; as the axe, chisel, 
knife, pin, needle, and shoemaker's awl. The angle 

of the wedge is rendered more or less acute, according to the pur- 
pose for which it is to be applied. In determining this, two things 
are to be considered ; the mechanical power, which is increased 
by diminishing the angle of the wedge ; and the strength of the tool, 
which is also diminished by the same cause. There is, therefore, 



gular prism. 
Fig. 94. 




272. Wedge, and manner of its use described. 

273. Advantage of the wedge. Geometrical form of the wedge. Instru- 
ments which act on the principle of the wedge. What two things are to be 
considered in determining the acuteness of the wedge ? What tools may be 
made most acute ? 



THE SCREW. 91 

a limit beyond which the sharpness of the instrument would de- 
stroy the requisite strength. 

Tools which act by pressure may be made more acute than 
those which act by the force of a blow ; and the softer, and more 
yielding, the substance to be penetrated, the less is the power re- 
quired to act upon it, and the more acute the wedge maybe made. 
Thus a cambric needle, and lancet, are manufactured in reference 
to the materials they are designed to work upon. An axe, for 
cutting wood, is more acute than a wedge for splitting iron. 

The Screw. 

274. The screw is a modification of an inclined plane. A 
straight road from the top, to the bottom of a high hill is, evidently, 
an inclined plane. If, instead of going directly up the hill, the 
road wound around it, in a spiral manner, it would still possess 
the essential characters of an inclined plane. The screw may be 
considered a winding wedge, bearing the same relation to a 

straight wedge, that a road winding up a hill, 
Fig. 95. bears to a straight road up the same hill. Let 

A B, represent a common round ruler, having a 
paper cut in the form of an inclined plane wound 
around it, the edge of the paper E C D, being 
marked by a black line : the ruler will then 
present the appearance of a screw, the line E 
C D, representing what is called the thread of 
the screw. 

275. The advantage gained by the screw, depends much upon 
tlje slowness of the ascent, that is, upon the number of turns or 
threads in a given distance. 

The screw consists of two parts, a solid cylinder, around which 
passes spirally the thread of the screw, and a hollow screw, with 
a similar thread, winding without it, exactly adapted to the inter- 
val between the turns of the thread of the solid screw ; and thus, 
either part being made to revolve, while the other is kept firm, 
pressure to almost any extent may be produced. The screw is 
generally used with a lever, which assists in turning it ; with 
this addition, it is a machine of great force, either in compressing 
bodies, or in raising great weights. It is to this mechanical power, 
that we are indebted for the common printing-press, and for most 
of the presses which are used in the arts and manufactures. 

276. L, represents the lever attached to the solid cylinder. 

274. Of what is the screw a modification ? 

275. On what depends much of the advantage gained by the screw ? Of 
what parts does the screw consist ? Use of the lever combined with the 
screw. 

276. Describe the screw. On what does the power of the screw depend ? 





92 NATURAL PHILOSOPHY. 

Fig. 96. The cylinder in ascending or descending the 

hollow screw, travels in a spiral line. The 
closer the threads of the screw, the greater 
the power of the instrument ; though, as 
more time is then required to traverse it, we 
find that here, as in the other mechanical 
powers, what is gained in power is lost in 
time. 

277. The screw acts with the combined 
power of the lever and the screw. The power 
of the screw is also affected by the length of 
the lever which turns it ; for the greater the 
circumference which the lever describes in one revolution, the 
more powerful is the action of the screw. In calculating the 
effects of the screw, the proportion should be estimated between 
the space described by the power in one revolution of the screw, 
and the space between any two of its contiguous threads. 
Thus, if the threads, a a, (Fig. 96,) be half an inch apart, 
and the screw be turned by means of the lever L, extending three 
feet from the center of the screw ; the advantage of such a ma- 
chine will be, as the number of half inches in the space described 
by the extremity of the lever, are to unity or 1. Now reckoning 
the circumference of a circle to be three times its diameter, the 
circumference described with a radius of three feet (because there 
are thirty-six inches in three feet) will be 36x2*=72x 3 = 216 
inches ; and twice that number, or 432 to 1, will be the measure 
of advantage afforded by the machine. 

278. It might be inferred that the power of the screw acted on by the lever 
could be indefinitely increased by extending the length of the lever, or by 
diminishing the interval between the threads of the screw. But a very long 
lever would be inconvenient, and extremely thin threads would be broken 
by the pressure when any considerable force should be applied to turn the 
screw ; so, that beyond certain limits, the lever cannot be lengthened, nor 
the distance between the threads of the screw shortened. 

Hunter's compound screw increases the efficiency of the power 5040 
times. The micrometer screw by the fineness of its threads, combined with 
other mechanical advantages, affords the means for measuring the fibre of a 
spider's web, the size of microscopic insects, or other objects too minute to 
be perceived by the naked eye. It has been adapted to the microscope. 

279. The ancients understood the use of complicated machinery. Plu- 

* The radius is half the diameter of a circle ; therefore 36 multiplied by 
2 makes the whole diameter 72 inches ;— this being multiplied by 3, shows 
the circumference to be 216 inches. 

277. How does the length of the lever affect the power of the screw? 
How is the power of the screw estimated ? 

278. Can the power of the screw be indefinitely increased ? Hunter's 
screw. Micrometer screw. 

279. Use of complicated machinery by Archimedes. Describe the ma- 
chine in which five mechanical powers are introduced. 






FRICTION. 



93 



Fig. 97. 



torch states that Hiero, king of Syracuse, was greatly astonished at seeing 
the philosopher Archimedes, Hitting on the sea shore and drawing into port, 
with one hand, a largo ship, heavily laden. According to the historian, this 
was done by gently moving the handle of a machine called polyspaston, or 
pulley. 

" The figure represents five mechanical powers combined to form a machine 
Cor drawing a ship upon the stocks to be repaired. 

The handle of the 
winch BC=:18 inches. 
The distance of the 
threads on CD=:1 inch. 
The diameter of the 
wheel ED-4 feet. 

The diameter of the 
axle EF=1 foot. 

G is a fixed, and H a 
movable pulley, the 
number of strings=4. 
Height of the plane 
equals half its length. 
Allowing a man to 
turn on the handle B 
with a power equal to 
100 lbs., how much 
force could he exert 
on the ship ? 

By rule given, 100 lbs. exerted at B would become, at D,.... XH309. 76 
And siuce the diameter of the wheels is four times that of the 
axle, 




Again, 
pulley, 



this is rendered four-fold by the four strings of the 



Finally, this is doubled by the plane, 

Hence, the force exerted on the ship would amount to 
3611)12 lbs., or more than 16 1£ tons."* 



X4 

45239.04 



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LECTURE XV. 



FRICTION. 



-MOVING POWERS. GENERAL REMARKS UPON MA- 
CHINERY. 



280. Friction is that resistance to a moving body which is 
caused by inequalities of surface. No substance is perfectly- 
smooth ; surfaces which appear so to the naked eye, as polished 

* Olmsted. 



280. What is friction ? Are any substances perfectly smooth ? 



94 NATURAL PHILOSOPHY. 

steel or glass, are found, when examined with a microscope, to be 
rough and uneven, like the face of a file. When substances move 
in contact, the prominence of one passing into the depressions of 
the other, occasion more or less resistance to motion. 

281. Friction wears upon the surface of bodies constantly in 
motion, and thus, in process of time render the various parts of 
machines unfit for use. Cohesive attraction between substances 
in contact, is another impediment to motion, though not equal to 
that caused by the ordinary inequalities of surface. Friction is 
diminished by making smooth the surfaces which are to come in 
contact ; but this must be done within certain limits, for great 
smoothness brings the bodies into such close contact as to pro- 
duce a considerable degree of cohesion. Less friction is produced 
when the substances which rub against each other are of different 
kinds, than when of the same kind ; as copper slides over brass 
more easily than over copper. Axles of steel are thus made to 
revolve on brass ; and in watches, the steel axles are often made 
to play in diamond, or some very hard mineral. The skater, with 
his steel skates, moves more rapidly over ice, than he could move 
over polished steel. 

By covering the rubbing surface with oil, tar, or soap, fric- 
tion is diminished. The axles of carriage and spinning wheels, 
and machines of all kinds, require the frequent application of these 
lubricating substances. 

282. The friction between rolling bodies is much less, than 
between those that drag. In certain kinds of wheel-work, the 
axle is made to revolve on small wheels, called friction-rollers. 
Sleighs are made to move on runners of steel, which slide over 
snow paths with little friction. In descending steep hills, it is 
common for drivers of carriages to lock the wheels, thus changing 
the rolling to the dragging motion. By increasing friction, the 
velocity of the descent is impeded.* 

288. Friction is proportioned to the quantity of matter in a 
moving body, and not to the extent of surface. Thus a brick with 
sides of unequal width, is found to meet with no greater resistance 

* The traveller on the " National road" over the Alleghany mountains, may- 
observe the " breaks" affixed to the stage coaches to produce the effect de- 
scribed. 



281. Effect of friction upon machines. Cohesive attraction impedes mo- 
tion. How may friction be diminished ? Friction less when the substances 
are of different kinds, than when of the same kind. Examples. Oil, &c, 
used to diminish friction. 

282. Difference in the degree of friction between rolling and dragging 
bodies. Friction rollers. Increase of friction impedes velocity 

283. Friction proportioned to the quantity of matter. Example. 



FRICTION. 



95 



Fig. 98. 




from friction, when moving on the broader, than when on the nar- 
rower side. If the pressure be increased by laying weights upon 
the brick, the amount of friction will also be increased, and in an 
equal proportion to the increase of weight. 

284. The degree of friction in moving bodies, may be ascertained as fol- 
lows; suppose a box, B E, to be laid upon a table, T T. Let a silken cord, 

fastened to the bottom of the box, be carried 
over the table and pulley at P, the scale, D, be- 
ing suspended by the cord. If no resistance 
were offered to motion, it is evident that the 
smallest weight, attached to the cord, would 
draw the box towards P. But the friction which 
always exists, prevents a small weight from 
drawing the box at all. But let weights be put 
in the scale D, until a sufficient force is obtain- 
ed to overcome the friction without giving the 
box an accelerated motion ; such a weight ia 
equivalent to the amount of friction. Now let 
the weight of the box, (which is supposed to 
have been previously ascertained; be doubled, by placing in it additional 
weights, the pressure will be doubled; and it will be found that the weight 
of the scale D, and its load, which was before able to overcome the friction, 
is now inadequate to this effect. Let additional weights be placed in the 
scale until the friction is counteracted as before, and it will be found that 
the whole weight necessary, for this is exactly twice the weight which pro- 
duced it in the former case. Thus it appears that a double amount of pres- 
sure produces a double amount of friction. 

285. When a heavy body is placed on an inclined plane it will 
have a tendency to slide ; and will, therefore, remain at rest on 
such a plane, only when the retarding cause of friction is greater 
than the tendency for motion caused by the inclination of the plane. 
The angle of inclination at which motion on an inclined plane 
commences, is called the angle of friction ; and, sometimes, the 
angle of repose. 

286. Friction may be considered a passive force. Its effects 
on machines in a state of equilibrium, are very different from the 
effects of the same force on machines in motion. In the one case, 
friction assists the power, in the other case, it opposes it. Thus a 
weight placed on an inclined plane, will require a less power to 
support it, in consequence of the friction of the two substances ; 
and a weight suspended by a rope passing over a pulley, will re- 
quire a less weight to balance it, on account of the friction of the 
axle. But the case is reversed when a machine is to be put in 
motion ; for then, friction makes a still greater power necessary 
than would overcome the weight, itself. The amount of friction 
varies in the several mechanical powers ; in the lever it is very 



284. How may the degree of friction in moving bodies be ascertained? 

285. A heavy body on an inclined plane. The angle of friction, &c. 

286. The effect of friction on machines at rest and in motion. Friction 
varies in the different mechanical powers. 



96 NATURAL PHILOSOPHY. 

little. In the wheel and axle, the friction of the wheel is in pro- 
portion to the weight, velocity, and diameter of the axle ; for, the 
smaller the diameter of the axle, -the less will be the friction. In 
the pulley, wedge, and screw, the friction is great. 

287. Notwithstanding the inconveniences of friction in retard- 
ing the motions of machinery, it is of great utility. If all bodies were 
destitute of friction, it would be difficult for us to grasp, or retain in 
our hands, any solid substance. A knife, a pen, or a book, could 
not be held without such an exertion of muscular power as would 
be fatiguing. Without friction, it would be still more difficult to 
use our feet than our hands ; the pavement, or ground, would be 
more slippery than ice ; and if shoes offered no resistance by 
friction, we should find it difficult to stand still, and much more so 
to walk. 

Friction offers an advantage in rubbing, scouring, polishing, 
and grinding. 

288. Besides the mechanical powers which we have enume- 
rated, there are other means of varying and accumulating force 
which might be considered as mechanical powers. Of these, are 
hammers, threshing -flails, clubs, slings, dec, which enable a con- 
tinued moderate effort to overcome a great resistance. 

Moving Powers. 

289. In liquids, and aeriform bodies, we find some of the most 
effective powers for moving machinery. The mechanical powers 
are of inestimable advantage to man, in enabling him to accom- 
modate the various forces of nature to the work which he has to 
perform. Thus he makes the running stream, the water -fall, the 
wind, and steam, turn his mills, impel his vessels, and even carry 
him over the ground, whither he would go. The heavy mill-stone 
is turned, and the most delicate fibers of cotton and silk are twist- 
ed, by these inanimate agents, which man has pressed into his 
service. 

Gravitation, or weight, affords the means of originating motion 
for many important purposes. By the proper application of this 
power, is maintained the regular motion of wheel work, as in a 
common clock, where the downward pressure of the weights keeps 
the machinery in motion. Elasticity gives force to various me- 
chanical agents. Elastic metals, such as steel, manufactured into 
springs, form the moving power in watches and various other kinds 

287. Utility of friction. Examples. 

288. Other means of varying and accumulating force. P^xamples. 

289. Liquids and aeriform bodies are moving forces. Examples. Motion 
obtained by gravitation, elasticity and heat. 



REMAHKS ON MACHINERY. 97 

of machinery. Heat, from its tendency to expand bodies, maybe 
ranked among the moving powers. 

290* The application of the natural strength of man, must have 
preceded the employment of all other moving powers ; but the 
force of brute animals was, by man, early made subservient to 
his convenience. Oxen and horses appear to have been employ- 
ed in the labors of the tield, in the most remote periods of anti- 
quity ; and the ass, camel, and elephant, are mentioned in the 
Scriptures and in other ancient records as beasts of burden. The 
mechanical effects produced by the muscular exertions of living 
beings cannot be estimated with the same precision as those of 
other moving powers, such as steam, water, gravitation, &c. The 
force of human exertion differs according to the manner in which 
it is applied. It has been estimated by some ingenious experi- 
ments, that the labor of a man employed in working a pump, 
turning a crank, ringing a bell, and rowing a boat, might be esti- 
mated respectively, by the numbers 100, 167, 227, and 248. 
From this it appears, that in working a pump the man labors to 
the least advantage ; and that rowing a boat is the most advan- 
tageous mode of applying human strength. The strength of a 
horse, in any given time is reckoned equal to that of five men. 
The strength of the elephant is computed to be equivalent to that 
of six horses. He will carry 3000 or 4000 pounds, and move at 
the rate of a slow trotting horse, traveling with ease 40 or 50 
miles in a day. 

General Remarks upon Machinery. 

291. From what has now been learned, with respect to me- 
chanical powers, the student will be prepared to understand some 
general principles relating to their use. These powers do not, 
in many cases, save labor, but they enable one man by working 
longer, to do what many men might perform in a short time. Thus, 
by means of a tackle, having ten folds of rope, one man may raise 
a weight which it would require ten men to raise without pulleys. 
But if the weight is to be raised a yard, ten men might raise it by 
pulling at a single rope and walking one yard, while the one man 
at the tackles, must walk ten yards. Therefore, to accomplish 
the same amount of labor, we have, in the one case, the time and 
strength of one man for ten minutes, while in the other, would be 
required the time and strength of ten men for one minute. A 

290. The strength of man and brute animals. Animal strength not so uni- 
form and precise as other moving powers. The efficacy of human strength 
depends on the manner of its application. Examples. 

291. Mechanical power enables one man to do the labor of many. Ex- 
amples 

9 



98 NATURAL PHILOSOPHY. 

printer with his screw, may press a sheet of paper against types, 
so as to take off a clear impression, whereas, without the press, 
the strength of fifty men would scarcely be sufficient ; and these 
fifty men would be idle and superfluous, except just at the time 
when the press-work is to be done. The screw may therefore be 
said to do the work of fifty men, since it saves the expense of 
keeping this number to perform what one man can now do. 

292. Machinery often enables a man to exert his whole strength, 
when without this assistance, he could employ but a part of it. 
Thus, in winding thread, he can turn one spool with one fiftieth 
part of the force which he is capable of exerting ; while, by means 
of machinery, he may turn fifty spools, in the same time, though 
with an increased amount of exertion. 

Females are greatly indebted to science for labor-saving ma- 
chines of various kinds. The carding machine has superseded 
the tedious and laborious use of hand-cards, giving the wives and 
daughters of farmers not only an exemption from severe toil, but 
more leisure for mental improvement. 

There is also an improvement in the common spinning wheel. 
An additional small wheel, and short band near the spindle, so 
much increases the velocity of the motion which twists the thread, 
as greatly to facilitate the operation of spinning by hand. But 
carding, spinning, and weaving, are now mostly performed through 
the agency of complicated machinery, moved by water or steam. 
The tending of these machines affords support to vast numbers of 
individuals. A wonderfully increased value is hereby given to 
human exertions. 

293. Machinery is useful in changing the direction of motion. 
The two varieties of motion most common in Mechanics, are the 
rectilinear and circular. In rectilinear motion, the several parts 
of a moving body proceed in parallel straight lines with the same 
speed. In circular motion, the several parts revolve round on axis, 
each performing a complete circle, or similar parts of a circle, in 
the same time. Each of these two kinds of motion may be either 
continued or reciprocating. In a continued motion, the parts move 
constantly in the same direction. In reciprocating motion, the 
parts move alternately in opposite directions. 

Continued rectilinear motion, is seen in the flowing of a river, 
the blowing of wind, the motion of an animal upon a straight road, 
and in the perpendicular fall of bodies. Reciprocating rectilinear 

292. A man's whole strength brought into use by machinery. The card- 
ing machine. The double wheel-head. Carding, spinning, and weaving by 
machinery. 

293. Difference between rectilinear and circular motion. Continued and 
reciprocating motion. Continued rectilinear motion. Reciprocating recti- 
linear motion. Continued circular motion. Reciprocating circular motion. 



REMARKS ON MACHINERY. 



99 



motion is seen in the rod of a common pump, as it rises and falls, 
and in the piston of a steam engine. Continued circular motion 
is seen in the revolving of wheels of all kinds, and in turning a 
crank as in the windlass used for drawing water. Reciprocating 
circular motion, is seen in the pendulum of a clock, and the balance 
wheel of a watch. 



Fig. 99. 




Fiff. 100. 



294. By means of machine- 
ry, a power having any one of 
these four varieties of motion, 
may be made to communicate, 
either the same kind of motion 
changed in its velocity or direc- 
tion, or either of the other kinds 
of motion which we have enu- 
merated. 

Rectilinear motion changed to 
circular. — The continued rec- 
tilinear, or straight forward mo- 
£-_ tion of water, produces the cir- 

cular motion of the water wheel. 
The straight, downward pressure of the 
foot upon a board communicating by a crank 
with the common spinning wheel, causes its 
rotary motion. The turning lathe of the car- 
penter, is also an instance of straight motion 
changed into circular. The alternate rising 
and falling of the piston of a steam engine 
by means of a crank, communicates motion 
to the wheels. 

295. Circular motion changed to rectili- 
near. The turning of an axle will wind up a 
rope, and thus lift a weight in a straight line. In the screw, the 
lever, which has a continued circular motion, causes the screw to 
advance with a continued rectilinear motion. 

296. Machines of different kinds are in use in every family, as 
the churn, washing machine, apple-paring machine, coffee mill, 
and clock ; while every town and village, has its grist mills, saw 
mills, and carding machines : and no one can go far in any sec- 
tion of our country, without hearing the busy hum of the " factory," 
where woollen and cotton fabrics, paper, &c. are produced at a ra- 
pid rate. The observing young student in mechanical philosophy, 




291. May these varieties of motion be modified or varied ? Motion of the 
water wheel. The common spinning wheel. 

295. Examples of circular motion changed to rectilinear. 

296. Machines in family use, mills, &c. 



100 NATURAL PHILOSOPHY. 

can never, therefore, be at a loss for examples or illustrations of the 
science. Whether he travel by land or by water, or sojourn in 
city or country, he will see in every motion, either of animate or 
inanimate objects around him, something to remind him of the laws 
and principles which he has already learned, or to suggest new 
applications of them. Even his own frame, in every motion of its 
muscles, is a living and moving example of the great laws of me- 
chanical philosophy. 



LECTURE XVI. 

THE PENDULUM. 

297, The oscillation or vibration of the pendulum is the effect 
of gravitation. This simple instrument, not only affords the means 
of ascertaining the variation of the force of attraction in different 
latitudes, thus furnishing a standard of weight, but its vibrations 
give the most accurate method of measuring time. 

■p. ,~, 298. Let P C represent a pendulum 

consisting of a heavy body, P, attach- 
C ed to a wire, which is fastened at the 

point C, and is movable around it. If 
the body P were left free, or not retained 
by the wire, it would fall in the line P 
B, vertical to the earth's center ; but being 
thus retained, it is forced to describe the 
arc P A, which is the segment of a circle, 
P of which P C is the radius. The body P 
acquires a velocity in falling through P A 
that has a tendency, when it arrives at the 
point A, to carry it off in the tangent A D ; 
but being prevented from moving in a straight line by centripetal 
force, viz : that of the wire, which continually draws it towards 
the center, it is forced to describe the curve A E. In the pendu- 
lum, we see an illustration of the effect of gravitation in accelera- 
ting and retarding motion ; thus from P to A, or downwards, the 
pendulum moves with accelerated motion, while from A to E, or 
upwards, the motion is retarded, until the force of projection being 
overcome by gravitation, it descends with accelerated velocity to- 

297. Cause of oscillation. Use of the pendulum. 

298. Explain the motion of the pendulum. 




THE PENDULUM. 101 

wards A. Were it not for the resistance of the air and the fric- 
tion of the suspending line on the point of suspension, or some 
other accidental obstruction, a pendulum once set in motion would, 
like the planets in their orbits, continue its motion forever. 

299. Each swing of the pendulum is called a vibration, or oscil- 
lation ; these vibrations are described in equal times, what- 
ever be the extent of the arc passed through. Thus this simple 
instrument, by means of its connection with a few wheels, has 
become a time -keeper, warning us at every vibration, that the 
number of our allotted moments upon earth is becoming less 
and less. 

300. The philosopher Galileo was led to the invention of the 
pendulum, by observing the motion of a chandelier hanging from 
the wall of a church in Pisa. Seeing that when put in motion, it 
vibrated with uniformity, as to time, he was led to make experi- 
ments that established what is termed the law of isochronism,* 
or equality of time. 

301. Though the resistance of the air passed through by the 
pendulum at each vibration, does, in fact, weaken the vibration, so 

that every successive arc of a circle de- 
Fig. 102. scribed becomes somewhat lessened ; yet, 

A as the rate at which it moves, becomes slower 

as the space passed through is shorter, a 
large vibration is performed in the same 
time as a smaller one. Thus the ball B, 
suspended from the point A, moves from 5 
to 5, from 4 to 4, &c. in the same time as 
from 1 to 1 ; for, in proportion as the arc 
described is more extended, the steeper are 
its beginning and ending, and the more rap- 
idly the pendulum falls, and passes through 
the intermediate space. 
802. Every person of common observation must have noticed the 
wheels, weights, and pendulum, which belong to that curious ma- 
chine, a clock. The weight is attached to a cord which is wound 
round a cylinder called the barrel, and this barrel revolves on an 
axis. The suspended weight pressing downwards by the force 
of gravitation, draws upon the cord, which, gradually unwinding, 
moves the barrel. This motion is communicated to a small 
wheel, which, in its turn, communicates motion to a series of 

* From the Greek isos, equal, and kronos, time. 

299. Vibrations in equal times. 

300. Observations of Galileo. What is meant by Isoclironism ? 

301. Cause of the equal time of vibrations. 

302. What belong to a clock? Describe the action of the weights, its 
office, &e. 

9* 




102 NATUKAL PHILOSOPHY. 

large and small wheels. Thus, the office of the weight is to 
turn all the wheels, and keep the pendulum (the axis of which is 
attached to the machinery,) in motion. When the pressure of the 
weight has drawn all the cord from the barrel, the clock stops. 
It may be " set going," or put in motion again by " winding up ;" 
that is, raising the weight by winding the cord around the barrel 
wheel, so that its gravitating force may again act upon the ma- 
chinery. 

303. We have already observed that a pendulum, once set in 
motion, would continue to vibrate were it not for certain opposing 
forces, viz. friction, and the resistance of the air, and would thus, 
without the aid of machinery, afford an exact measure of time, and 
an instance of perpetual motion. But some degree of force must 
be applied, to counteract the impediments to its continued motion ; 
and this force is obtained in the clock, by the pressure of the weight 
upon the cord. 

304. The main spring of a watch, answers the same purpose 
for communicating motion to the wheels, as do the cord and weight 
of a clock. The motion of the wheels of the clock is regulated by 
the pendulum, the motion of the wheels of the watch is regulated 
by the balance wheel. 

305. The motion of the hands is produced by the operation of 
ingeniously contrived wheels, fitted with teeth or cogs, so as to 
give motion to other wheels. One wheel having sixty such teeth, 
turns round once for sixty beats of the pendulum of the clock. 
The pendulum being so graduated as to beat seconds, one revolu- 
tion of this wheel is therefore made in sixty seconds, or one minute. 
An index fixed on the axis of the wheel, and projecting through 
the dial plate, is called the second hand of the clock. Another 
wheel is so connected with this, and the number of teeth so pro- 
portioned, that it turns sixty times slower, in order to carry a min- 
ute hand upon its axis ; and another wheel, by moving twelve times 
slower than that which carried the minute hand, is fitted to carry 
upon its axis the hour hand. 

306. Though " a clock is nothing more than a piece of mechan- 
ism for counting the swings of a pendulum," its advantage to man- 
kind is incalculable. Before its invention, men made artificial 
divisions of time in various imperfect methods, as by observing the 
regular dropping of water, the running of sand in the hour-glass, 
the shadow upon the sun-dial, &c. 

307. The length of the pendulum influences the time of its vibra- 

303. Force which keeps the pendulum in motion. 

304. Moving power in a watch — how is the motion in a watch regulated? 

305. Motion of the hands of a clock, how produced ? 

306. DhTerent modes of dividing time. 

307. Effects of lengthening the pendulum. Rule. 






THE PENDULUM. 



103 



Fig. 103. 




tion. Long pendulums vibrate more slowly than short ones, be- 
cause in corresponding arcs of circles, the ball of the long pen- 
dulum has a greater distance to pass over without having a steeper 
line of descent. If a pendulum, b a, be twice as 
long as another extending from b to e, it has twice 
the length to fall in its descending arc c a, as the 
other in its arc d e ; its movement will, therefore, 
be proportionally slower, according to the laws of 
gravitation ; that is, the time of the vibration will 
increase, as the square root of the length of the pen- 
dulum increases. If a pendulum one yard long, 
would make one vibration in one second, a pendu- 
lum four yards long, would vibrate once in two 
seconds, and a pendulum nine yards long, would 
vibrate once in three seconds, &c. 

308. The pendulum being usually of metal, is liable to varia- 
tions in length, from changes in temperature. In summer, being 
dilated or lengthened by heat, it vibrates more slowly than in 
winter, when, owing to the loss of caloric, it becomes shortened. 
Though the difference in the length of pendulums, and their con- 
sequent variation in time, is slight, it is of some importance, and 
various methods have been invented for obviating this irregularity. 
The length of a pendulum for vibrating seconds, in our latitude, is 
about thirty-nine inches. 

309. Since the vibration of the pendulum depends on the force 
of gravity, it follows that pendulums of the same length will vi- 
brate quicker when the force is greater. As the force of gravi- 
tation decreases as the distance from the earth's center in- 
creases, the vibration of the pendulum is slower upon the sum- 
mit of a high mountain than at its base. Any change in the 
force of the earth's attraction would, at once, vary the motion of 
the pendulum and prevent clocks from measuring time truly. In 
mines and deep caverns of the earth, though the pendulum is 
nearer the earth's center, the weight or gravity of the great mass 
of matter above, counteracts the central force, and attraction is 
therefore less than at the surface, and the pendulum vibrates 
more slowly. 

310. At the equator, the oscillations of the pendulum are slower 
than at any other point on the surface of the earth. This is owing 
to the form of the earth, which is bulging at the equator, and flat- 
tened at the poles, so that at the equator, the pendulum is far- 



308. Effect of temperature upon the pendulum. Length of a pendulum 
for seconds. 

309. Why the pendulum vibrates slowly on high mountains and in mines. 

310. Vibration at the equator. 



104 NATURAL PHILOSOPHY. 

thest from the center of the earth. The centrifugal force arising 
from the earth's motion, being also greater at the equator, has an 
effect to counteract the force of gravity. 

311. As the attraction of gravity is in proportion to the mass 
of matter, the quantity of weight attached to the pendulum, or the 
weight of its ball, has no effect upon the speed of vibration, except 
that which results from the resistance of the air. Experiments 
upon the pendulum, to be perfectly accurate, should, therefore, be 
made in a vacuum. 

312. The pendulum is not only of importance in regulating our 
divisions of time, and thus enabling us to systematize the business 
of life, but it affords the only sure mode of determining the varia- 
tion in the force of gravity in different latitudes, and at different 
heights. While it serves to amuse the child by its regular and 
continuous motion, it furnishes problems to the Philosopher, the 
solution of which requires the most intricate and profound mathe- 
matical calculations. 



LECTURE XVII. 



LOCOMOTION. 



313. Before closing the subject of mechanics we will consider 
the wonderful improvement, which this sciencee, aided by chem- 
ical discoveries of the nature and powers of steam, has effected in 
the rapidity of locomotion.* 

314. But, first, let us imagine the state of our own country, 
when our ancestors planted themselves here. The Indian had 
no roads ; his wandering life led him to traverse mountains and 
forests for game, and to follow the winding stream for fish. Fine 
roads and convenient carriages, would, to him, have been super- 
fluous. In the first journey from Plymouth, Mass., to Windsor, 
Conn., undertaken by our pilgrim fathers, they traveled through a 

* From two Latin words, locus, place, and motio, motion, signifying mo- 
tion from a place. 



311. Weight of the ball does not affect vibration. 

312. Why should experiments be made in a vacuum ? 

313. The science of mechanics connected with locomotion. 

314. Former state of our country in regard to roads. 



LOCOMOTION. 105 

trackless wilderness, bearing the wife of their minister, Mr. 
Hooker, on a litter. Several weeks were required to perform the 
journey. There were no bridges across the streams, and the 
weary travelers must seek for fording places directed by accident 
alone ; searching their way through the defiles of mountains, and 
meeting often with obstacles which obliged them to retrace 
their steps and take a new direction. In perils from savage men 
and ferocious beasts, they encamped at night beneath the canopy 
of heaven, trusting in the protection of that Being whom they 
sought to worship in sincerity and truth. 

The first roads and bridges constructed in our country, were of 
a rude and temporary nature. Carriage roads were unknown 
long after the paths were traced leading from one settlement to 
another. 

315. Science furnishes rules for the construction of roads ; and 
in these days, when new roads are to be made, they are not as 
formerly left to chance, or the rude skill of the ignorant ; but civil 
engineers are called upon to survey and graduate them, according 
to the laws of mechanical philosophy. 

" The province of the engineer, is to surmount the difficulties 
presented by friction, gravitation, collision and road surface. 
He must consider the traffic upon the intended line of road, and 
determine whether a saving of tractive power, will compensate 
for the outlay of capital required to form the road. The quality 
of the road must depend on the means of making and supporting 
it ; and there are situations in which it would not be judicious, 
even to attempt to make any road at all."* 

316. From common roads for carriages, we have gradually 
passed to canals, McAdamized roads, and rail-ways. In canal 
conveyance, a difficulty has been suggested, founded on the well 
known law of mechanics, that the resistance offered by water to a 
boat in motion, increases as the squares of the velocity. But Gor- 
don suggests, that if canal boats were differently constructed, their 
speed might be greatly increased, without increasing the resist- 
ance of the water. He would have the horizontal, or propelling 
force, so great, as to allow little opportunity for the force of gravi- 
tation to act upon it, and thus cause the boat to shim the surface 
of the waters, rather than, by suffering it to become deeply im- 
mersed, to have the resistance of a large body of the fluid to over- 
come. Thus, in the case of a number of cannon balls laid in a single 

* Gordon on Locomotion. 

315. Science important in the construction of roads. Circumstances to be 
considered by the engineer. 

316. Supposed difficulty in canal conveyance. How obviated. 



106 NATURAL PHILOSOPHY. 

tier, upon a level surface, and in contact with each other, if one 
should attempt to move the furthermost ball, by a slow motion in a 
line with the others, he must communicate motion to them all, and 
therefore be obliged to use a force much greater than would have 
been necessary, if, with a quick motion, he had drawn the ball 
above the others, and moved it over their surfaces. 

It is said, that on the Paisley canal, in Scotland, boats are moved 
by horse power, at the rate often miles an hour ; and it is sug- 
gested that by the use of steam instead of animal power, the velo- 
city may be increased, and the expense of locomotion lessened.* 

317. McAdamized roads are intended to prevent the resistance 
of surface. Stones broken into small fragments are laid upon the 
road to the depth of ten inches. Mr. McAdam considered, that a 
road thus constructed would be smooth and durable ; and that the 
nature of the soil below the coating of broken stones, was of no 
importance. This kind of road, though an improvement upon the 
ordinary turnpike, does not answer all the valuable purposes sup- 
posed by its projector. It is found to be, not only very expensive 
in the outset, but to require almost constant repairs. 

318. In the construction of rail roads, and the application of 
steam power to locomotion by land, we see the greatest triumph 
of modern improvement. Instead of the nerves and sinews of ani- 
mals, strained to their utmost extent to drag their ponderous loads, 
is substituted the power of the light elastic steam, an agent which 
can suffer no pain, and consumes no food. About the year 1770, 
Oliver Evans, an unlearned American mechanic, happening to 
make some observations on the elastic power of steam, conceived 
the idea that it might be turned to some account in moving ma- 
chinery. He was confirmed in his opinions by experiments. But 
when he predicted, that " the child was then born who would pass 
in carriages propelled by steam, at the rate of at least fifteen miles 
an hour," he was thought to be insane. Rail roads were first 
made in England ; they are now numerous in our own country, 
and by their means, and the aid of steam boats, a rapid communi- 

* Could we see on our great western canals, packets moved swiftly by 
steam, the scene would be far more pleasant than that exhibited by the slow- 
motion of jaded animals ; and a great advantage would be afforded in the 
increased facilities for locomotion and transportation. But it remains to be 
proved that Mr. Gordon's plan of avoiding the resistance of a large portion 
of fluid can be acted upon by means of any construction of boats, or peculiar 
mode of applying the motive power. Dr. Lardner, and some other scientific 
men, do not admit the practicability of any plan of the kind. 



317. McAdamized roads. 

318. Rail roads. Rapid traveling. Effects of rapid communication upon 
the prosperity of the country. Mode of constructing rail-ways. 



LOCOMOTION. 



107 



tion and intercourse is maintained thoughout its vast extent. The 
effect of this connection of places, once considered distant, is very 
important upon the wealth, comfort, and improvement of society. 
The country merchant, after purchasing his goods in one of the large 
cities, is not obliged to lie out of his capital, as he was when de- 
pendant upon the former slow modes of conveyance. If there be, 
at any time, a deficiency of any article in one part of the country, 
there is soon a rapid pressure of it flowing from those places 
where it is more abundant. A quick and general circulation of 
the produce of the earth, of articles of commerce, and of literature, 
is to a nation, what the healthy circulation of the blood is to the 
human system. 

We shall, hereafter, consider the manner in which steam is 
made to act as a moving power. We are now to notice its ap- 
plication to land carriage. Rail roads, or rail-ways, are made by 
laying horizontal bars of iron for the wheels of the cars to run on. 

The wheels are confin- 
Fig. 104. ed within the track by a 

flange which constitutes 
a part of their structure. 
The figure shows a loco- 
motive engine, with the 
wheels upon an iron rail 
way. The engine is fol- 
lowed by a tender, con- 
taming the engineer, 
with a supply of fuel and water. The train of carriages or cars 
attached, varies in number according to the number of passengers 
and amount of goods to be conveyed. 

319. When horses are the motive power, the less the wheels 
of the carriage to which the horse is harnessed, or those of the 
train following, adhere to the rails, the more easy it will be to 
move the train. But when a locomotive is to be impelled by the 
action of a steam engine in turning the wheels, if the resistance by 
gravity and friction be greater than is the force with which the 
wheels adhere to the rails, the engine will only revolve the wheels 
to which it is geared ; these will turn upon the rails, while the 
locomotive and whole train attached to it will remain stationary. 
To prevent this, different contrivances have been resorted to. 

320. Another step in locomotion, which seems about to be ta- 
ken, is that of the construction of steam carriages to run on com- 




3 th th dh £h dh E 



319. Adhesion of the wheels of the carriage to the rails a disadvantage 
when horses are the moving power. The case is different when a carriage 
is moved by a steam engine. 

320. Steam carriages for common roads. 



108 NATURAL PHILOSOPHY. 

mon roads, which shall go up hill and down, without any aid from 
machinery, other than the proper regulation and adjustment of the 
motive power. In England, many trials have been made to this 
effect, and a committee appointed by the House of Commons have 
reported favorably upon the project. The Committee gave it as 
their opinion that the advantages of steam power are not confined 
to the greater velocity thereby obtained, nor to its expense, as 
compared with that of horse power. But they think, in relation 
to the use of horses, that danger as well as expense, is increased 
by increasing velocity. In steam power, on the contrary, there 
is no danger of being run away with ; and the risk of being over- 
turned, is greatly diminished. Steam is found to be perfectly con- 
trollable, and capable of exerting its power to retard the motion in 
going down hills. It can be stopped or turned with the slightest 
exertion, and under circumstances where horses would be unman- 
ageable. Sounds or sights can have no power to affright this un- 
conscious agent which labors so effectually for mankind. 

If we could believe all that is predicted with respect to improve- 
ments in the application of steam, we may expect to see the day 
when the farmer's plow and market wagon, the pedler's cart, 
stage coaches, and private carriages will be moved by steam 
power ; and when steam for the purposes of locomotion, will be as 
common in every family, as are now a coffee mill, a patent churn, 
or a washing machine. 



PART III. 

HYDROSTATICS. 



LECTURE XVIII. 

MECHANICAL PROPERTIES OF LIQUIDS. 

321. There are, in nature, three distinct forms under which 
substances exist ; viz ; solids, liquids, and gases. Wood, water, and 
air, are examples of each class. Many of the mechanical laws 
which govern solid bodies, equally apply to liquids and gases ; but, 
as the latter have properties peculiar to themselves, it follows that 
each class is subject to its own peculiar laws, 

322. Under the general name of fluids are included liquids and 
gases ; the former are called non-elastic fluids, the latter, elastic 
fluids. 

323. The name of non-elastic fluids was given to liquids from 
the supposed fact that they were in no degree elastic, or compres- 
sible. Common air, steam, and other elastic fluids, are easily 
compressed, and on removing the pressure they expand to their 
original dimensions. This may be proved by pressing an inflated 
bladder. A bag of leather or India rubber, filled with water, and 
secured so that none of the liquid can escape, may be burst by 
forcible compression, but cannot be made to exhibit any sensible 
degree of contraction. Water, from its powerful resistance to 
pressure on all sides, was long considered as perfectly incompres- 
sible. An experiment made by some Philosophers at Florence, 
in the sixteenth century, confirmed this opinion. A hollow globe 
of gold filled with water and closed tight, was subjected to the 
powerful action of a screw-press. The water did not become com- 

321. Substances exist under three forms. Liquids and gases subject to 
peculiar laws. 

322. How are fluids divided ? 

323. Are liquids compressible 1 Experiments of Philosophers at Florence. 
Experiments of Perkins. 

10 



110 NATURAL PHILOSOPHY. 

pressed so as to occupy less space, but forced its way through the 
pores of the dense metal, and appeared like dew on the outer sur- 
face of the globe. Though this experiment was long considered 
conclusive proof that water cannot be compressed, later trials have 
shown that though its resistance to pressure is very great, it will 
yield, in some degree, under a certain weight. Experiments by 
Mr. Perkins, before the Royal Society of London, proved that a 
weight of 2000 atmospheres, (or a weight 2000 times as great as 
that of the atmospheric column,) diminished the bulk of water one 
twelfth part. 

But so inconsiderable is the degree to which liquids can, by any 
ordinary force, be compressed, that in all calculations respecting 
their action, they are regarded as incompressible Jluids. 

324. Solid bodies are subject to the power of cohesive attrac- 
tion in a much greater degree than liquids ; and the latter, in a 
greater degree than gases. The parts of a solid are connected 
together, so as to form one whole ; their force of gravity is there- 
fore centered in one point, which, if supported, prevents the whole 
from falling. In fluids, (although each atom has its own center 
of gravity,) the pails have not a common center of gravity, there- 
fore, as soon as a vessel is filled with any liquid, each additional 
drop runs off at the sides. 

825. The same substance may exist in the form of a solid, liquid, 
gas, or vapor. Ice is solid ; expose it to the influence of heat, and 
it assumes the liquid state ; an additional quantity of heat causes 
this liquid to become steam or vapor. Mercury is commonly seen 
in the form of a very dense liquid, quick-silver; but it may, like 
water, be condensed or frozen by exposure to a very low temper- 
ature, and made to boil or evaporate, by subjecting it to a great 
degree of heat. 

326. Hydrostatics, (from two Greek words, udor, water, and 
statos, standing,) is the science which treats of the weight, pres- 
sure, and equilibrium of liquids. 

327. Liquids afford an example of a state in which cohesive 
attraction is exactly balanced by the repulsive principle, heat. 
Water, by losing a certain portion of heat, is given up to the power 
of attraction, and, its particles cohering, it becomes a solid. By 
the addition of heat, the particles of water are driven to a greater 
distance, and the liquid changes to a light and expansive vapor. 
Oil, deprived of heat, congeals into a solid ; by the addition of heat, 
it becomes the gas, known in chemistry, as olefant or oil-gas. 

324. Liquids have less cohesion than solids. Proof. 

325. The same substance may exist in different forms. 

326. Of what does Hydrostatics treat ? 

327. Attraction and repulsion balanced in liquids. 



IIYDKOSTATICS. 



Ill 




328. The particles in liquids being freely movable among each 
other, yield to the least disturbing force. Those particles are 
supposed to be round and smooth, because they move easily and 
without friction. This supposition accounts for some properties 
of liquids which could not, otherwise, be well explained. For 
instance, water will take up a certain quantity of sugar without 
being increased in bulk ; again, a certain portion of salt may be 
added and yet the original bulk of the water remain the same. 

Let us suppose a vessel to be filled with cannon balls ; 
it is evident that it can hold no more balls ; but a quan- 
tity of small shot might find their way into the spaces 
existing between the large balls ; and when no more 
shot could be added, sand or ashes might be introduced 
to fill up the spaces between the shot ; and water might 
afterwards be added to fill up the spaces between the 
particles of sand. It is a well known fact that a cask 
tilled with ashes, will receive a large quantity of water, 
il gradually, so as to give time for the water to penetrate the 
interstices between the particles of ashes. Now admitting the 
spherical form of the particles which compose liquids, we can per- 
ceive the reason that some liquids will receive into the spaces be- 
tween them, smaller particles of other substances. 

Pressure of Liquids, 

329. Liquids press not only downwards like solids, but upwards 
and laterally, and the pressure is equal in all directions. 

330. W* will first show the upward pressure of liquids. Let 
ABC, represent a bent tube of glass. Now if by means of a 

funnel, you pour sand into a tube at A, the sand 
after filling the lowest part of the tube, will rise, 
until the side A B is full ; after which, if sand be 
poured into the funnel, it will run over the top of 
the tube at A. If instead of sand, you pour water, 
or any other liquid, into the tube, at the mouth A, 
you will find the fluid to preserve a level on both 
sides of the tube ; a small quantity would fill the 
bottom, and would rest at the line d ; an additional 
quantity would carry the height of the fluid to the 
line e, and another portion would raise it toy. 
This experiment proves the upward pressure of li- 
quids, since the water, by this force, is raised in the side C B, con- 
trary to the laws of gravitation. 

328. Particles in liquids. Liquids will take up portions of certain sub- 
stances without any increase of bulk. 

329. Pressure of liquids. 

330. Upward pressure illustrated . Exp. 1.. 




112 NATURAL PHILOSOPHY. 

Fig. 107. 331. Exp. 2d. Let the glass jar or cylinder, A B, 
be nearly filled with water, while a glass tube, a b, 
(open at the top,) is pressed so closely upon the bottom 
of the jar as to prevent the entrance of any of the liquid ; 
the tube being raised a little, the upward pressure of 
the water will cause it to rush up into the tube until it 
is on a level with that in the jar. On taking the tube 
out of the jar, the water runs out, and air rushes in to 
supply the vacuum. Stop the tube at a with a cork, 
and plunge it again into the water ; the liquid now, rises 
no higher than b. This is because the tube was filled 
with air, and matter being impenetrable, no two sub- 
stances can, at the same time, occupy the same space. 
If the tube were not closed at the top, the water, being 
the heavier substance, would press the air upward and 
take its place, as proved by the experiment. It may 
be asked, " if the tube be filled with air, and if this cannot escape, 
how can the water enter the tube ?" We answer that air being 
compressible, the upward pressure of the water has forced that 
which before filled the tube, into a smaller space ; for, it is evident, 
that as none has escaped, it must be contained in the space be- 
tween the cork and the top of the water, b. The same quantity 
of matter being compressed within less space, it follows, that the 
air in the tube is more dense than before compression. 

332. Though air is thus easily compressed, great force is re- 
quired for the compression of water : let a glass tube be corked 
at the top and filled with a colored liquid ; hold a piece of paste- 
board close to the other extremity of the tube, to prevent the escape 
of the liquid, and plunge the tube into a tumbler of water ; if 
you remove the pasteboard, and plunge the tube to any depth of 
water, the colored liquid will still keep its place, and will not, like 
air under similar circumstances, show that the upward pressure 
of the water has any power to cause it to occupy less space. 



LECTURE XIX. 

PRESSURE OF LIQUIDS. 

333. The lateral or side pressure of liquids, is equal to the 
pressure either upward or downward. That the lateral pres- 

331. Exp. 2. What causes the water to rise in the tube ? Exp. 3. Why 
does not the water rise as high as in experiment 2. 

332. Water not easily compressed. 

333. How is the lateral pressure of liquids proved ? 



PRESSURE OF LIQUIDS. 



113 




Fig. 108. sure is equal to the pressure downward, may be il- 
lustrated by the following experiment. Let the ves- 
sel, A B, be filled with water, and let two orifices of 
equal dimensions, a and b, be made, the one at the 
bottom, the other at the side of the vessel. Let the 
water run into two receivers, and it will be found at 
the end of a given time, that the quantity of liquid 
which has escaped, is equal in both receivers. This 
proves that the lateral pressure is equal to the pres- 
sure downward. The opening at the side is made 
quite at the lower part of the vessel ; were it higher, 
the liquid would not flow out with equal velocity, as, 
the greater the weight of the column above, the greater the force 
of the downward pressure ; therefore, in this experiment, the per- 
pendicular height of the two orifices must be equal, 

334. From the force of pressure in different directions, 

Fig. 109. water poured into a bent tube, called a syphon, will stand 

j^ equally high in both sides. If the communicating tubes 

P^ are of different diameters, still the fluid stands at the same 

height in both ; therefore a portion of liquid, however 
vj ) small, will resist the pressure of a portion however large, 
and will balance it. 

335. In a common tea pot, we see an illus- 
tration of this law, as water poured into the 
body of the vessel, will rise to the same height 
in the spout as in the body of the vessel ; and 
if poured into the spout, the small column in 
the latter would still be forced to balance the 
whole column, in the main portion of the 
vessel. 

336. So strange did this law of nature appear, when first dis- 
covered, that Philosophers termed it the " hydrostatic paradox." 
This phenomenon may be explained on mechanical principles. 
Opposite forces have been shown to be equal when their momenta 
are equal ; that is, what is wanting in weight may be made up in 
velocity. In mechanics, it is an established law, that the power 
and weight balance each other, when the power moves as much faster 
than the weight, as the quantity of matter is less. Let this law be 
applied to the case which we are now considering. 

Suppose the aperture A, (Fig. Ill,) to be ten times the size of B ; 
then a quantity of water one inch in height in the spout B, would rise 



Fig. 110. 




334. Liquid in a bent tube. In a tube varying in diameter. 

335. What law illustrated by Fig. 110 ? 

336. What is the hydrostatic paradox ? How may it be explained on me- 
chanical principles ? 

10* 



114 



NATURAL PHILOSOPHY. 




Fig. 111. in the vessel, A, but one tenth part of an inch ; or 
a certain quantity of liquid would rise through a 
space of ten inches in the tube B, while it would 
rise but one inch in the vessel A. Thus we find that 
there is in reality, nothing more wonderful in the hy- 
drostatic paradox, than that one pound at the long end 
of a lever should balance ten pounds at the short end. 
337. The velocity of columns of water, when in motion, being as 
much greater in the smaller columns, as in the larger columns the 
quantity of matter is less, it follows that in vessels of various sizes 

and shapes, connect- 
Fig. 112. ed with a common re- 

servoir, the liquid will 
rise to the same level, 
f g, in all ; here the 
water being consid- 
ered the weight, and 
pressure the power, 
the weight and power 
may be said to be in 
equilibrium, where the fluid is on a level in each of the vessels. 
Thus we find that, in all situations, fluids at rest maintain a level 
or horizontal position. 

338. The whole mass of liquid, and the sides 
of the containing vessel are affected by the slight- 
est compression. 

In a quantity of liquid subjected to compresssion, 
the whole mass is equally affected ; and, hence, if a 
cork be forcibly driven into a bottle full of water, 
the pressure will be felt alike in every portion 
J|L of the liquid, which will press against the sides 

of the bottle in all directions, causing it to break 
at that point which is weakest, however situ- 
ated in relation to the mouth or where the force was 
applied. 

339. The pressure of a column of liquid is in proportion to its 
perpendicular height. 

By this proposition we mean, that the pressure of any liquid 




Fig. 113. 




337. Why do liquids rise, in various shaped vessels, to an equal height, 
when connected with a common reservoir ? 

338. Does compression on any portion of a fluid affect other portions in 
the same vessel ? Experiment. 

339. Proposition. What is meant by " pressure according to height?" 
Suppose the containing vessel wider or narrower towards the top, or of an 
equal diameter throughout. Experiment to prove that one pint of water 
may be made to balance twenty pints. 



PRESSURE OF LIQUIDS. 



115 



Fig. 114. 



upon the bottom of a vessel, is not according to the quantity con- 
tinued but according to the weight of a perpendicular column, hav- 
ing for its base the bottom of the vessel, and for its height the depth 
of the liquid. If the vessel become wider towards the top, as in 

A, the pressure at the base 
is less than the weight of 
the whole liquid, it being 
denoted by the shaded 
perpendicular column, the 
base of which is b a. If 
the vessel become narrow- 
er from the base, as at B, 
the pressure at the base is 
greater than the weight of 
the liquid, as denoted by the dotted lines. When the vessel is, 
throughout, of an equal diameter, as in C, the pressure on the 
bottom is equal to the weight of the whole liquid. 

Suppose two vessels to 




Fig. 115. 




have their bases equal, but 
the vessel A holds twenty 
times more than the vessel 
B ; that is, A holds twenty 
pints, while B, holds but one 
pint. Each vessel has a 
brass bottom, D, opening 
like the lid of a box. A 
pulley, F, supports a weight, 
E. Let the vessel A be sup- 
ported by its sides, and water 
poured in until the pressure 
of the liquid begins to raise the weight, and of course to open the 
lid-like bottom, when the water will begin to escape. Let the 
height, a b, be marked, at which the surface of the water stands 
when the bottom begins to give way. Try the other vessel, B, in 
the same manner, and it will be seen that when the water is at 
the height, c d, the weight will begin to rise, and the bottom to 
fall. Let c d be continued to b, and it will be seen that the two 
lines a b and c d are on the same horizontal plane ; therefore the 
height of the two columns are equal. Here we see, that equal 
weights are overcome, in the one case by twenty pints of water, 
and in the other case by one pint, and therefore that one pint of 
water may be made to balance twenty pints. 

340. The law we have now explained and illustrated, viz ; that 



340. Why will a cask when filled with liquid, burst with the weight of a 
very small column of liquid. 



116 



NATURAL PHILOSOPHY. 



Fig. 116. 



the pressure of a column of liquid is in proportion to 
its perpendicular height and base, explains why a 
cask when filled, may be burst by the additional 
weight of a few ounces of liquid. Suppose the 
cask A B to have C D, a tube several feet in 
length, inserted at its top ; on filling the tube 
with water, the compressive force will' be in pro- 
portion to a column, the height of which is the 
height of the tube, and the base, the top of the cask ; 
therefore, the pressure upon the cask is the same 
as if a column, equal in diameter to the whole 
diameter of the cask, extended to the top of the 
tube. 

341. Many of the convulsions of nature, mani- 
fested by broken and scattered rocks, have been 
caused by hydrostatic pressure. Since* a column 
of water, only a few feet in height, is capable of 
bursting a hogshead, by the force of its pressure, what force might 
not be exerted by a column of water contained in the fissure of a 
mountain, extending several hundred feet in depth. " Suppose in 
the bowels of a mountain there should be an empty space of ten 
yards square, and only an inch deep, on an average, in which a 

Fig. 117. 





r 5v^ 






thin layer of water had lodged, so as to fill it entirely ; and sup- 
pose that in the course of time, a small crack of no more than an 
inch in diameter should be worn from above, 200 feet down to the 
layer of water ; if the rain were to fill this crack, the mountain 
would be shaken, perhaps rent in pieces, with the greatest vio- 
lence, being blown up with a force equal to the pressure of above 



341. Effect of water pressure in rending mountains. 



PRESSURE OF FLUIDS. 



117 



Fig. 118. 




5022 tons of water, though only 2£ tons had been actually 

applied."* 

312. The hydrostatic or water -bellows, is an ar- 
ticle of philosophical apparatus which illustrates 
the pressure of fluids. A long tube communicates 
with the body of the bellows ; this consists of two 
oval boards, connected by folds of leather like the 
common bellows. When the tube is filled with 
water, the pressure upon the upper part of the bel- 
lows will be such, as not only to raise the board, 
but to sustain heavy weights placed upon it. The 
force of the pressure, (when the tube is full,) will 
be equal to the weight of a column of water, whose 
base is as the surface of the bellows, and whose 
height is as the length of the tube. It will readily 
be perceived that the pressure of a certain quantity 
of water may be increased by making the circum- 
ference of the bellows larger, and the tube smaller and longer ; 
as, by so doing, the base and height of the column will be enlarged. 
If the tube hold an ounce of water, and have an area equal only 
to one thousandth part of that of the upper board of the bellows, 
one ounce of water in the tube, will raise, or balance a weight 
of a thousand ounces resting on the bellows. 

343. If mercury were substituted for \#Lter, in a similar ma- 
chine, the effect of the fluid pressure would be fourteen times 
greater, because the same bulk of mercury is fourteen times 
heavier than water. Air, which is an elastic fluid, may also pro- 
duce powerful effects in the same manner ; — if a bellows were suf- 
ficiently large in diameter for a man to stand upon, he might, by 
blowing into a perpendicular tube with his mouth, raise his own 
weight by the pressure of the air acting upon the bellows. 

344. The principle of hydrostatic pressure has been applied to 
the construction of a very powerful press, called the hydrostatic or 
water-press. So great is the force thus obtained, that with a ma- 
chine no larger than a common tea-pot, a bar of iron iriay be out 
as easily as a strip of pasteboard with a pair of shears. Instead 
of the tube of the bellows, the water-press has a small pump; and 

* See Treatise on Hydrostatics, Library of Useful Knowledge. 

342. Explain the principle on which the hydrostatic bellows is construct- 
ed. Force of the pressure of the column of liquid in the tube. Suppose the 
circumference of the bellows were larger, and the tube of less diameter but 
of greater length. 

343. What would be the effect of substituting mercury for water in a simi- 
lar machine 1 Might not air be used instead of water or mercury ? 

344. Application of the principle of hydrostatic pressure. Power of the 
water-press. 



118 



NATURAL PHILOSOPHY. 



Fig. 119. 




for the body of the bellows is substituted a pump barrel and 
piston. 

345. In the seventeenth century, Pascal, a man no less celebrated 
for learning than for piety, discovered the 
principle of hydrostatic pressure ; he as- 
serted that an engine might be construct- 
ed, acting through the force of a column 
of water, by means of which, one man, 
pressing on a small piston, might resist 
the efforts of a hundred men brought to 
bear on the surface of a large piston. 
This imaginary machine was termed by 
its' projector, " a new machine for mul- 
tiplying forces to any required extent." 
It was not, however, until more than a 
century afterwards, that any practical 
application was made of this force. 
" Bramah's hydrostatic press" (Fig. 119,) consists of solid masonry, or strong 
wood work, E F, firmly fixed, and connected by uprights with a cross-beam. B 
represents a strong table, moving vertically in grooves between the uprights ; 
and any substance to be pressed or broken, is placed in the space above it. 
B is supported beneath by the piston A, which works within the hollow 
cylinder L, and passes through a collar N, fitting so closely as to be water- 
tight. From the cylinder passes a small tube with the valve opening in- 
wards at I. D is a lever^which works the piston of a small forcing pump, 
C H, by which water is crrawn from the reservoir G, and driven into the cyl- 
inder L, so as to force up its piston A. At K is a valve, which being re- 
lieved from pressure, by turning the screw which confines it, a passage is 
opened for the water to flow from the cylinder, through the tube M, into 
the reservoir G, allowing the piston to descend. 

The effective force of such a machine must be immensely great, combi- 
ning as it does, the advantages of solid and liquid pressure. The amount 
of the latter is to be estimated by the relative diameters of the two pistons ; 
so that if the piston H be half an inch in diameter, and the solid cylinder or 
piston A one foot, the pressure of the water on the base of the piston A, will 
be to the pressure of the piston H on the water below it, as the square of 1 
foot or 12 inches, 12X12=144, to the square of ^-an inch, 5X5=25 ; that is, 
as 144 square inches to \ of a square inch, or in the ratio of 576 to 1.* To 
this must be added the advantage afforded by the lever-handle of the forcing- 
pump, depending on the relative lengths of its arms ; and supposing the 
power to be thus increased tenfold, the effect of the machine will be aug- 
mented in proportion, or will become as 5760 to l.t 



* The pupil will need some knowledge of decimals, to understand this 
statement ; 5 is the decimal of half an inch, — the square of 5 is 25 or \ of a 
square inch. Multiplying 144 by 4, we obtain the number 576, and thus the 
advantage here obtained by liquid pressure, is as 576 quarters of inches to 1 
quarter of an inch. 

t Moffat's Book of Science. London. 



345. Describe the water press of Bramah. 
vantage of a water-press of known dimensions. 



Mode of estimating the ad- 




HYDBOSTATICS, 119 

346. The hydrostatic prosa is applied to various important pur- 
poses ; to compress hay, cotton, and other bulky commodities, 
which may thus be made to occupy on ship-board, a space twenty 
or thirty times less than in their natural state. »It is also used to 
raise great weights, to uproot trees, and to cut hard substances. 

347. The pressure upon any particle 
Fig. 120. f a liquid, is in proportion to its depth 
A 13 below the surface. Thus, the inclined 

column B C, being of the same perpen- 
dicular height as the straight column 
A C, both exert the same pressure upon 
the base C. Suppose e and f to be half 
the distance from the surfaces A and B, 
the pressure upon them is but half as 
great as upon a particle at C. 

348. The cause of this increase of 
pressure is evident. The fluid atoms be- 
ing subject to the laws of gravity, the 

upper layer presses upon the next, which, with double its own 
weight, presses upon the third layer, and thus the pressure is con- 
stantly increasing with increasing depth. For this reason, pipes 
for aqueducts should be made stronger in proportion to their depth, 
as also the sides of canals, embankments, &c. The lateral pres- 
sure being equal to the downward, it follows that the sides of a 
canal, or embankment, receive the greatest pressure nearest the 
bottom. 

349. The weight of a solid or cubic foot of water, is 1000 oun- 
ces, or 62£ pounds. Now at the depth of 8 feet, as the pressure 
on a square foot is equal to a column of water whose base is 1 
foot, and whose depth is 8 feet, the solid contents of such a column 
are 8 cubic feet. Therefore, as one solid foot of water is 62£ 
pounds, and this number multiplied by 8 is 500, it follows that a 
column of water 8 feet deep, causes a pressure equal to 500 pounds ; 
at 16 feet the pressure is double, or equal to 1000 pounds, and so 
on in the same proportion. Thus at the depth of 64 feet, or eight 
times 8 feet, there is a pressure of 4000 pounds, which is ascer- 
tained by multiplying 500 by 8. From these facts, we may form 
some idea of the vast pressure of the water of the ocean, which is 
supposed to be, in some places, four or five miles deep. The pres- 

346. Uses of the water-press. 

347. Pressure proportioned to depth. 

318. Cause of increase of pressure. How should this principle affect the 
construction of aqueduct pipes, canals, &c. 

349. Weight of a solid foot of water. Pressure of a column of water 8 feet 
deep. Of a column 64 feet deep. Pressure of the Ocean. Why deep sea8 
cannot be sounded. Experiments on the pressure of water. 



120 NATURAL PHILOSOPHY. 

sure at the depth of one mile, is equal to the weight of 330,000 
pounds. This explains the fact so well known, that in deep seas, 
it is impossible for the mariner to learn the exact depth by sound- 
ing, because the lead, which is attached to the cord he uses, floats 
at a certain depth. 

A common square glass bottle (containing only air) if corked and 
sunk in water to the depth of sixty feet, will be crushed inwards 
by the pressure. If the bottle be first filled with water, then cork- 
ed and let down to any depth into the sea, the bottle will not be 
broken, because the pressure of the liquid within resists the ex- 
ternal pressure. At a certain depth, the cork, owing to the com- 
pressibility of water, will be forced into the bottle ; and this, in 
whatever direction the mouth of the bottle may point, whether 
downward, upward, or laterally ; for pressure, as has been already 
explained, is equal in all directions. 

350. The downward pressure of the particles of a fluid is occa- 
sioned by gravitation ; the lateral pressure results from the down- 
ward pressure pushing out at the side, with equal force, the con- 
tiguous particles. For it must be remembered, that the fluid parti- 
cles are not supposed to be piled exactly above each other, (as at A,) 
but to be arranged as cannon balls are usually piled 
Fig. 121. one above another, (as at B.) If the particles be- 
low had not a tendency upward equal to the weight or 
downward pressure of the particles above, they could 
not support them. Their upward tendency may be 
considered as derived from the pressure around them. 
351. Even water itself, which was long supposed incapable of being com- 
pressed into a smaller space, is found unable to resist the powerful pressure 
of its own element. An apparatus has been invented, consisting of a hollow 
brass cylinder, which being filled with water and closely stopped, is sunk to 
a certain depth, at which the stopper will be driven inwards. Means are 
contrived for ascertaining how far the stopper is driven in at different depths. 
The brass cylinder being full when it was closed, the stopper could not have 
been pressed inwards, unless some portion of the water within was expelled, 
or the whole compressed in bulk ; and since the cylinder allowed no portion 
to escape, it follows that the liquid was compressed, and this compression 
is found to become greater at greater depths. The same experiments have 
been repeated with the hydrostatic press. It has been proved, that under a 
weight of 1500 pounds to the square inch, water loses one 24th part of its 
bulk, and its specific gravity is increased in the same proportion. 

Level surface of Liquids, 

352. That liquids, when left free to arrange themselves accord- 
ing to their own laws, always maintain a horizontal position, is too 

350. Cause of downward and lateral pressure. Of upward pressure. 

351. Experiment for proving the pressure and compressibility of water. 
Experiment with the hydrostatic press. 

352. Curved surface of the Ocean. Why not perceptible. Tendency of 
water to seek its level. 



IIYDUORTATICS. 



121 



familiar a fact to need any illustration. Yet though we speak of 
the level of the sea, it must be recollected that from the spherical 
form of the earth, the surface of the ocean must be curved. And 
however small any extent of surface may be, it is not, strictly speak- 
ing, exactly level. But from the size of the whole globe of the 
earth, the general curvature of those portions within the scope of 
our vision, is too small to affect our sense of sight, or to alter the 
mechanical laws of nature. From this tendency of liquids to settle 
into a level, arises the glossy smoothness of the calm lake and still 
fountain, which reflect the surrounding images as faithfully as the 
most perfect mirror. If these waters be disturbed, as soon as the 
exciting cause ceases, they again resume their smooth and equal 
surface. Water from highlands is continually seeking to make its 
way downward, in order to find a level. Lakes and ponds, in ele- 
vated countries, are constantly pressing against their boundaries, 
and when these give way in the slightest degree, fearful inunda- 
tions of the country below are the consequence. The beautiful 
valleys and picturesque glens, which we now behold, were, proba- 
bly, once filled with water, which, in seeking its level, found some 
outlet of escape into a lower region. 

353. It is upon this level-seeking principle in water, that aque- 
ducts are constructed, as whether conveyed in artificial pipes, or 
natural channels, water will rise as high as its source. Suppose 
a reservoir, A, to be on an elevation at a little distance from a 
city or village, the water may be brought in pipes or aqueducts, B, 

Fig. 122. 




through a valley, and then up an acclivity, until it reaches a height 
equal to that of the reservoir ; thus it may be distributed by com- 
municating pipes to every street. The ancients, who were at great 
expense in the construction of aqueducts, often carried water over 



353. Principle on which aqueducts are constructed. 
of the ancients. 

11 



Aqueduct bridges 



12*2 KATUMAl -CV. 

valleys by means of aqueduct bridges, instead of conducting it 

through pipe?. For tLi? s?me have supposed that they 

were iornorant of that law by which liquids rise in pipes or chan- 
nels as high as their sir. B .:: as :zey did. i\\ 
pipes laid in the earth, for conducting water, it is probab. 
adopted the more expensive mode of arcades, on account of their 
greater permanency. For, as the pressure in pipes is greater in 
proportion to the depth of the water below the reservoir, it follows, 
that in descending great declivities, the force of this pressure upon 
the pipes is so great, as ultimately to burst the strongest material. 



LECTURE XX. 

SPECIFIC GRAVITY. 

354. All bodies of equal bulk have not the same weight. A 
of cork weighs -r>s than a piece of hard wood of the 

size, and a piece of lead of the same dimensions, weighs more 
than either. Thus each different kind of matter has its specific, 
or peculiar weight, which is expressed by the term . 
gravity. 

355. The absolute gravity of any substan fal weight, 
or the force with which it presses downwards : the relative grav- 
ity, or, which is the same thing, specific gravity, is the weight of 

..pared with others of equal bulk. I 
frees of density, that substances thus differ in regard 
to gravity. The more dense a body is. the more particles of mat- 
ter are contained within a certain bulk, and the great- 
cific gravity. For example, lead is a very dense, and cork, a po- 
rous body. 

Water is the siandard for estimating the relative, or spe- 
cific gravity of solids and liquids. That is, if a certain bulk of 
any substance be found to have exactly the same weight as the 
same bulk of water, its specific gravity is called 1 : if it be twice 
as heavy as the same bulk of water, its specific gravity is called 2, 
and so on. The specific gravity of gold is about 19 : that is, gold 
is about 19 times heavier than wafer. 

Wd gbt not depending on balk. Meaning of the term specific gra- 
vity. 

355. Absolute and relative gravity . C arose of difference in gravity. 

356. Standard for estimating specific gravity. What is meant when the 

specific gravity of any substance is stated as 1, 2 7 & 









. Rule for ascertaining rarity. Weigh the body 

iir>t in air, (that is, in the c mmon mode,) th< El in water; 

find how much weight it I _hed in water: now 

divide the former weight by the lass sustained, and the result will 
be the specific gravity of the substance .. or it> relative 

weight when compared with the weight of w 

The figure represents an 
Fig. 123. hydrostatic balance. > 

suppose c to be a solid inch 
of gold suspended from the 

a of the scale b 
let its weight be ascertain- 
ed, by pur ts in 
the opposite scale, o, and 
suppose it to be 19 ounces : 
2d, place beneath the scale 
6, a glass vessel j tartly filled 
with water. the irold is buoy- 
ed up by the liquid with a 
force proportioned to the 
weight of the water which it displaces, and is found to lone one ounce 
in weight, or to weigh in water but 16 ounces ; 3d. according to the 
rule already given, divide 19, the weight of the gold out < jftbe water, 
by 1, the loss of weight sustained in th and the quotient 
its specific gravity. That is. a piece of gold, weighing 19 
ounces, occupies the same space as a portion of water weighing 
one ounce, or, in oth^r words, gold is 19 times heavier than water. 
359. It is found that this dijjerence between the weisht of the 
gold in air and in water, gives the weight of a quantity of waiter 
equal to tie* bulk of the metal. This rule is founded on a law in 
Hydrostatics, that a solid body immersed in ,any liquid, n 
weighs less than it does in air. but that the difference corr - 
exactly to the weight of the liquid which it displaces : and. it is 
evident, that the liquid thus displaced, is of the same bulk as the 
solid ; since the latter fills a space which be: \actly tilled 
by the liquid. 

359. The heavier a body is. the le-s water will a given weight 
of this body displace. If we take of gold, silver, tin, and ma 




357. How may the specific gravity of a substance be ascertained ! Hy 
drostatic balance. What is the first step in the process of finding the specific 
gravity of a substance ? What the -2d step ? What is the 3d step I 

358. What quantity of water will weigh as much 1 loses of its 
weight in water ? How does it appear that the liquid displaced is of the 
same bulk as the solid which has taken its place ? 

359. By what experiments can it be proved that the heavier a body is, the 
:er will a given weight displace ? 



124 



NATURAL PHILOSOPHY. 




piece of each, weighing one ounce ; the ounce of gold will be 
the smallest of all the pieces, and the marble the largest ; for the 
specific gravity of gold is 19, while that of marble is but 2 ; tin, 
though lighter than gold, is heavier than marble ; and silver is 
heavier than tin ; therefore the ounce of silver would be greater 
in bulk than the gold, and less than the tin : the ounce of tin would 
be larger than that of silver, and smaller than that of marble. 

Take four tumblers of 
Fig. 124. equal size, A B C D, 

and containing equal 
quantities of water, be- 
ing filled up to the hori- 
zontal line ; put the 
ounce of gold into D, 
that of silver into C, 
that of tin into B, and 
the marble into A, the water will be raised or displaced in propor- 
tion to the bulk, and not to the weight of the substances immersed. 

360. Whatever may be the form of different substances, their 
exact bulk, or size, is ascertained by weighing them in water, as 
from the ease with which the liquid particles move, water accom- 
modates itself to cavities and protuberances. Lumps of minerals 
of the most irregular forms, may be weighed in water, and their 
specific gravities ascertained ; that is, their weight and bulk com- 
pared. By this means, the mineralogist accurately distinguishes 
the various genera of minerals. If all substances could be easily 
formed into regular, solid figures, their comparative gravity could 
be determined, by simply weighing them in the usual manner ; 
thus, if we suppose a cubic inch of gold, weighing 19 ounces, a cubic 
inch of silver 10^ ounces, and one of tin about 8 ounces, we could es- 
timate their relative weight accordingly ; but most natural substan- 
ces, such as diamonds and other precious stones, and common mine- 
ralogical specimens, are of various, and irregular figures. It is, 
therefore, very important that there should be a method of esti- 
mating their exact bulk, and comparative weight. 

361. Specific gravity of solids lighter than water. 

The cases we have considered, are of such substances as are 
heavier than water, and therefore sink in it. When a body is 
lighter than water, its specific gravity is ascertained by attaching 
to it some heavier substance which will cause it to sink, and the 



360. Bulk of irregular masses ascertained by weighing them in water. 
Advantage of this to the mineralogist. If substances were of regular forms, 
how could their specific gravity be ascertained ? Most natural substances 
irregular in their forms. 

361. Mode of ascertaining the specific gravity of substances lighter than 
water. Experiment to prove the specific gravity .of wood. 



SPKCII'IC CKAVITY. 



absolute weight and specific gravity of this additional substance be- 
ing known, it is eas) to find, by subtracting from the Lose of weight 
of the mixed mass in water, the loss of the heavy body alone ; the 
difference is the loss of the lighter body. 

Suppose we wish to tind the specific gravity of wood, which, be- 
ing lighter than water, floats on its surface. The specific gravity of 
copper is known to be 9 ; suppose a lump of this metal, weighing 
one pound to be attached to a piece of wood. According to the 
method given lor ascertaining specific gravity, we have only to 
subtract from the weight of the whole mass in water, 9 for the 
whole loss of the copper, and the remainder of the loss of weight 
in water is that of the wood, or lighter body ; which loss being 
divided by the weight of the wood out of the water, the specific 
gravity of the wood is ascertained. 

Specific Gravity of Liquids. 



362. The specific gravity of liquids is ascertained 
Fig. 125. by means of a simple instrument, called an hydrome- 
ter* This is a hollow, floating bulb, B, of glass or 
metal, with a graduated tube, ad; the specific gravity 
of a liquid may be estimated by the depth to which the 
hydrometer, when plunged into it, sinks, or by the 
weight required to sink the hydrometer to a certain 
depth. Weights are suspended at c, for the purpose of 
sinking the instrument, and keeping it in a vertical po- 
sition. The weight necessary to sink the instrument to 
a certain mark on the tube, determines the specific 
gravity of the liquid into which it is plunged. As the 
resistance of fluids is in proportion to their density, it 
follows, that the hydrometer will sink deepest in those 
fluids which are lightest. This instrument is used by 
brewers and distillers, to determine the strength of their 
liquors. It is also used in salt manufactories, to test 
the strength of the brine. The deeper the hydrometer 
sinks in spirits, the stronger they are, because alcohol is specifically 
lighter than water ; and the less the spirits are reduced with 
water, the lighter they are, and, of course, the less resistance 
they offer to the pressure of the instrument. In brine, on the 
contrary, the instrument is borne up, salt water being heavier than 
fresh water, in proportion to the degree of salt which it holds in 
solution. 

* From the Greek words, udor, water, and metron, measure. 



362. Hydrometer. 



Use of the hydrometer. 
11* 



126 NATURAL PHILOSOPHY. 

363. It is related, by Dr. Arnott, that a merchant in China, who had sold 
a quantity of distilled spirits to the purser of a ship, according to a sample 
shown, went into his shop and added to each cask a quantity of water. — 
The spirit being delivered on board the ship was tested by the hydrometer, 
and found to be reduced. The Chinese ignorant of any human means by 
which the fraud could be detected, confidently denied it ; but on the exact 
quantity of water which had been added, being specified, he was seized 
with a superstitious awe, and, confessing his roguery offered to make ample 
restitution. When shown the instrument by means of which he had been 
detected, he was struck with admiration, and offered to purchase it at any 
price that might be demanded. 

364. There are many common facts, the philosophy of which can be un- 
derstood only by a knowledge of the different specific gravities of bodies. 
When a person lies in a bath, he feels himself borne up by the liquid around 
him ; but on going out, his limbs seem heavier than usual. The specific 
gravity of water being greater than air, causes the difference in the sen- 
sations, on being surrounded by one, or the other element. Water is said 
to have no weight in water ; thus a bucket in a well is made to ascend with 
a slight force until it reaches the surface of the water, after which its 
weight is sensibly felt. Many fishes are nearly of the same specific gravity 
as water, therefore, when lying inactive, they neither sink nor swim. It is 
said, that a certain king of ancient times demanded of the learned men of 
his court, an explanation of the fact that fishes had no weight in water ;* 
many profound theories were offered, but none seemed satisfactory. At 
length an unlearned man, consulting only the philosophy of common sense, 
balanced a vessel of water in scales, and putting a fish into it, showed that 
the weight in the vessel was increased by the whole weight of the fish. — 
For supposing the fish to be of the same specific gravity as the water, that 
is as 1 to 1, it was the same thing, as if a certain portion of water had 
been added, which in its own element wotdd lose no weight. 

365. Two columns of liquids of different specific gravities, bal- 

ance one another, when their heights are, inversely, as 
Fig. 126. their specific gravities. 

In the bent tube A B, when the height of the column 
B is as much higher than that of A, as the liquid B is 
lighter than the liquid A, the two columns will balance 
each other and remain at rest, at A and B. As the 
bases and heights of the columns of fluid, determine their 
force ; this force must of course vary, with the specific 
gravities of the liquids. Thus mercury having a specific 
gravity about 14 times greater than that of water, a co- 
lumn of mercury would balance a column of water 14 
~^^^ times higher than itself. 

366. " A body lighter than its bulk of water, will float, and with 
a force proportioned to the difference of specific gravity. If the 

363. Detection of fraud by means of the hydrometer. 

364. Why a person feels himself lighter in a bath. A bucket easily raised 
in water. Question of a certain king. 

365. When will two columns of liquids of different specific gravities bal- 
ance one another ? Example. Column of mercury balancing a column of 
water. 

366. Cause of bodies floating in water. Specific gravity of the human 
body. Cause of its sinking in water. 



SPECIFIC GKAVITY. 127 

Fig. 127. cylinder a b c d, be partly immersed in water, the 
upward pressure of the water on the bottom c d, is 
I, exactlj what served to support the water displaced 
Si by the body, viz. water of the bulk ofefc d. The 
body therefore, that it may remain in the position 
here represented, must have exactly the weight of 
the water which the immersed part of it displaces ; 
HIP 1 * and if it be lighter than this, it will rise higher, if 
heavier it will sink deeper.*" 
The specific gravity of the human body is very nearly the same as that of 
Water, and when the lungs are tilled with air, (which is lighter than water,) 
the body will not sink. But to Hoat upon the surface of water, it is neces- 
sary that a person should lie quietly, with the face upwards. By lifting up 
the head, as its weight in air is greater than in water, a downward impulse 
is given; and this is also the case with respect to throwing the limbs out 
of water. Thus the struggles of one who has accidentally fallen into deep 
prater tend to make him sink ; and the greater pressure of the liquid below 
the em-face by compressing the air in the lungs, renders it more difficult for 
the body to rise. 

367. The figure represents a glass jar nearly filled with 
Fin- 128 water, and covered closely with a piece of Indian rubber. 

There are three figures of glass, which being hollow within 
aud filled with air, are of less specific gravity than the wa- 
ter, and float on the surface. By pressing with the hand 
upon the elastic cover of the jar, a small portion of air 
which is between this cover and the surface of the water, 
is acted upon ; this pressure forces the water through cavi- 
ties in the feet of the glass figures into their bodies, and 
compresses the air within. Their increased specific grav- 
ity, causes them to sink. The cavity within the figure E, 
being greater than that within the figure D, the same pres- 
sure will force more water into E than into D, causing E 
to sink to a greater depth. For the same reason C does 
not sink as low as D. On raising the hand, as the pressure 
is then removed from the air between the cover of the jar 
and the water beneath, the whole mass of water is released 
from the pressure, and the elastic air within the figures by expanding, drives 
out the water which had been forced inward, and the figures again rise to 
the surface. 

368. That bodies heavier than water sink in that fluid, may 
seem to contradict the assertion that upward pressure is equal to 
downward pressure. But weight and pressure do not always mean 
the same thing. Thus when a stone is thrown into water, follow- 
ing the impulse of gravity, it makes an attempt to descend ; but it 
cannot do this without displacing as much water as is equal to its 
own bulk ; therefore it is resisted or pressed upward, by a force 

* Arnott. 

367. What causes the figures in the jar to sink ? Why do they not sink to 
equal depths? How can they be made to rise again to the surface? 

368. Weight and pressure not synonymous. Why does a stone sink in 
Water? 




128 NATURAL PHILOSOPHY. 

equal to as much water, as is equal in magnitude to the bulk of 
the stone ; but the weight of the water is less than that of the stone, 
therefore the force pressing against it upwards, is less than its ten- 
dency downwards, and consequently, the pressure of the water be- 
ing less than the weight of the stone, the latter will sink. 

369. The specific gravity of a body is sometimes stated in whole numbers 
and decimals, sometimes in fractions only. — As it is often important to be 
very accurate in ascertaining the specific gravity of substances, and as the 
numbers 1, 2, 3, &c, would not in many instances express this difficulty, 
the weight of water may be considered not only as a unit, but as 10, 100, 
1,000. Thus gold is a little more than 19 times heavier than water ; this 
may be expressed by a vulgar fraction, ^ ; or in decimals, either as 19.25, 
or 19.250, the fraction 25 being one fourth of a hundred, and 250 being one^ 
fourth of a thousand, the same proportion is expressed in both statements. 
If the weight ol water is estimated as a unit, then the specific gravity of 
gold, (which is nineteen limes and a quarter heavier than water,) should be 
expressed as 19^; if the weight of water is estimated as 100, then the spe- 
cific gravity of gold should be stated as 19.25, the decimal being the frac- 
tion of a hundred, &c. The specific gravity of pure alcohol is less than 
that of water; it is estimated as 797 — that is, considering water as 1000. — 
The specific gravity of milk is somewhat greater than that of water, it be- 
ing 1-032. Platina is the heaviest of all known substances; its specific gra- 
vity is 22, water being 1. The pure metals are the heaviest class of sub- 
stances, their specific gravity being from 5 to 22. The metallic ores being a 
mixture of earth and other substances with the metals, are lighter than the 
pure metals, although usually above 4. The precious sloues, as the dia- 
mond, emerald, &c, have a specific gravily between 3 and 4. Common 
minerals between 2 and 3. Some kinds of wood are a little heavier than 
water, as mahogany, which is 1,06; but generally wood is lighter than 
water. Cork has a specific gravity of .24. Hydrogen gas, the lightest of 
all known substances when compared to water, has a specific gravity of 
.00008, or eight one hundred thousandths. 

Discovery of Specific Gravity. 

370. Simple as appears the method of determining the specific gravity of 
bodies, it was not known until about 250 years before the Christian era. — 
Archimedes, a Philosopher of Sicily, surpassed all his predecessors in depth 
of research into the principles of mechanics and hydrostatics. He is cele- 
brated for his treatises on mathematics, and for various philosophical discov- 
eries and inventions. It is recorded in history, that Hiero, the king of Sy- 
racuse, having hired an artist to make for him a crown of pure gold, sus- 
pected the man had mixed with the gold given' him for that purpose, 
some metal less valuable, but the crown weighed as much as the gold the 
king had furnished, and he knew of no method of detecting the fraud, if 

369. Modes of stating specific gravity. How is the specific gravity of gold 
expressed? Specific gravity of Alcohol. Of Milk. Of Platina. Of Metals 
in general. Of Metalic Ores. Of the precious stones and common minerals. 
Of Wood. Of Hydrogen Gas. 

370. Time of the discovery of specific gravity. Suspicion of Hiero re- 
specting his crown. His application to Archimedes. The Philosopher's 
perplexity. His observation while bathing. His experiments with pieces 
of gold and silver. With the king's crown. How was he able to ascertain 
the quantity of silver added ? 



IIYDRAULICS. 129 

there had been one, and applied to Archimedes for assistance. The object 
was, (without melting the crown in order to separate the mixed metals, if it 
Wen really composed of such,) to ascertain, witliout injuring the workman- 
ihip of the crown, its quantity til' alloy. This could not be ascertained hy any 
rule then known, and the Philosopher was much perplexed. One day, 
jpou stepping into a full hath, he observed that a quantity of water flowed 
iver which appeared equal to his own bulk, and that his weight seemed 
,ess in the water than out of it ; he was struck with the idea that " a body 
olunged into a liquid, loses a weight equal to that of a mass of the liquid 
>f equal bulk," and leaping out of the bath, he ran through the streets 
shouting in the Greek language, " eureka ! eureka ! n "I have found it 
jut, I have found it out." He afterwards proceeded to test the truth of his 
.uiagiiied discovery, and to apply it to the case under consideration. He 
:ook two masses, one of gold the other of silver, and each of equal weight 
;o the crown ; having filled a vessel with water, he first dipped into it the 
nass of silver, and accurately determined the quantity of water which flow- 
k! out; he then made a similar trial with the gold, and found that a less 
piautity had flowed out than before. Thus he established the fact, that the 
)ulk of any mass of silver was greater than that of gold of the same 
veight. He then made the same experiment with the king's crown, and 
mind that, though its weight was the same as the mass of silver and the 
nass of gold, it displaced less water than the silver, and more than the gold. 
finis he ascertained that the crown was neither pure gold, nor pure silver. 
Jy determining the actual specific gravity, he was enabled to ascertain the 
(xact quantity of silver, which the artist had added to the gold to make the 
veight the same as the original weight of gold delivered by the king. 



LECTURE XXI. 

ON LIQUIDS IN MOTION, OR HYDRAULICS. 

371. The term hydraulics, (from two Greek words, udor, wa- 
er, and aulos, a pipe,) was at first used to signify the motion of 
vater in certain musical pipes, in^se among the Greeks ; it is 
tow applied in a more general sense to liquids in motion, in dis- 
inction from hydrostatics, or liquids at rest. The popular use of 
he term hydraulics, is chiefly confined to the consideration of 
pater-works, as pumps, fountains, engines, mills, and machines 
f various kinds, in which the power is derived from water in 
lotion. Water can be set in motion by its own gravity ; as 
yhen it descends from a higher to a lower level ; in which case, 
t will seek the lowest situation ; also by the pressure of con- 
en sed air, or by removing the pressure of the atmosphere, when 
t will rise above its natural level, and thus it may be forced to 
Teat heights. 

371. Definition of hydraulics. Popular use of the term. Causes of the 
notion of water. 




130 NATURAL PHILOSOPHY. 

372. The velocity with which water spouts out at an orifice in 
the side or the bottom of a vessel, is as the square root of the dis- 
tance of the orifice below the surface of the water. 

If, at the distance of one foot from the 
Fig. 129. surface, the velocity is 1, because 1 is 

the square root of 1 ; another orifice 
four feet from the surface, would give the 
velocity of 2, because 2 is the square 
root of 4 ; and, at 9 feet deep, there 
would be a velocity of 3, because 3 is 
the square root of 9. Suppose a vessel 
(see Fig. 129,) discharging its contents 
at three orifices. The liquid from the 
upper spout being near the surface, re- 
ceives but a slight pressure from the 
column above it, and flows with com- 
paratively slight velocity ; at the second spout, as there is a col- 
umn of greater depth above it, the liquid is pressed out with 
greater velocity ; and at the lowest spout, where the pressure is 
greatest, the velocity is also greatest. 

The force of the pressure does not depend upon the width of 
the containing vessel, but upon the height of the column of fluid. 
(Art. 334.) 

373. The liquid projecting from the side of a vessel describes 
the curve of a parabola : for two forces act upon the body in 
motion, viz., the uniform pressure of the incumbent liquid, and 
the accelerated force of gravity ; in respect to which, liquids fol- 
low the same law as solids. The random or horizontal distance 
of the three spouts of water (represented at Fig. 129,) is greatest 
at the middle spout, and equal above and below. The velocity of 
the lowest spout being greatest, we might suppose the random 
would be so, if we did not reflect that this spout reaches the hori- 
zontal level sooner than thosdftbove it. 

374. The velocity with which water issues from a spout, is uni- 
formly retarded as the surface of the column descends. Here the 
mechaniceJ law respecting liquids, is directly contrary to that of 
solid bodies falling freely by gravitation ; but it corresponds to the 
law respecting solid bodies thrown upwards, for the force of pro- 



372. Velocity of spouting fluids. Velocity of spouting fluids at different 
distances from the surface. Why is the velocity greatest at the lowest spout, 
as represented in the figure ? 

373. Why does the projected liquid describe the curve of a parabola? 
Where is the random greatest in the three spouts represented in the figure? 

374. Velocity of spouting fluids uniformly retarded. Spaces described by 
the descending columns. 



IIYDHO.STATU . 



131 



Fig. 130. 

A 



i i> greater in proportion to the perpendicular height of the 
column, and this is constantly diminished by the flowing out of the 
liquid. The spaces described in equal times by the descending 
surface of the liquid column, are as the odd numbers, 1, 3, 5, 7,9, 
eve, taken backwards; while, in solid bodies falling freely by gra- 
vitation, the spaces described are, us this series in an ascending 
order. Suppose a vessel tilled with water be divided into 25 parts, 
and having at the bottom an orifice lor letting off the liquid ; if, in 
one minute, the surface descend through 9 of these 
parts, in the next minute it will descend through 7 parts, 
in the third minute 5, in the fourth 3, and in the fifth 1. 
375. The Clepsydra, or water clock, is construct- 
ed on the principle we have just considered. If a 
cylindrical vessel of water be found to discharge its 
contents in a given time, by an orifice at the bottom, 
the sides of the vessel being divided by lines into 
equal spaces, these spaces become divisions of time. 
Thus, if the vessel A empties itself in six hours, 
divide it into 36 equal parts — lor the first hour mark 
off 1 1 parts, for the second 9 parts, for the third 7 
parts, for the fourth 5 parts, for the fifth 3 parts, and 
for the sixth hour 1 part. 

There are some subjects, as the steam engine, pump, and 
syphon, which might, with propriety, be considered un- 
der the head of hydraulics or liquids in motion ; but, in or- 
der fully to comprehend the principles on which they are 
constructed and on which their action depends, it is neces- 
sary to understand the nature and properties of air, which 
we are about to consider. 

Synopsis. 

376. 1st. Hydrostatics treats of the mechanical properties of 
now-elastic bodies, as water. 

2d. Liquids press equally in all directions. 

3d. A column of liquid presses in proportion to its perpendicu- 
lar height, and the base of the vessel containing it. 

4th. Specific gravity is the relative weight of equal bulks of 
different substances ; water being made the standard of compar- 
ison. 

5th. The science which teaches the laws of liquids in motion, 
is called hydraulics. 

6th. The velocity of spouting fluids is as the square root of the 
depth of the orifice below the surface of the liquid. 

375. Clepsydra, or water clock. Subjects connected with hydraulics and 
pneumatics. 

376. Synopsis of important pi-inciples in hydrostatics. 



// 




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9 


— 


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7 


— 


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— 


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3 




3 
9 



PART IV 

PNEUMATICS. 



LECTURE XXII. 

AERIFOKM BODIES. ATMOSPHERE. THE AIR-PUMP. 

377. The Greeks, under the term pneuma, included air, vapors, 
and gases of all kinds with which they were acquainted, and also 
the soul or spirit of man. From pneuma is derived pneumatics, or 
that science which treats of the mechanical properties of elastic 
or aeriform liquids. It is chiefly the phenomena of atmospheric 
air that we are now to investigate. 

378. Every one possessing any knowledge of chemistry knows 
that there are, in nature, several kinds of gas ; that these gases, 
by their union with each other, form water and air ; that with metals 
they form ores in various proportions, and that they exist in all ani- 
mal, vegetable, and mineral substances. But with gases, strictly so 
called, we have, in Natural Philosophy, little to do ; as their part 
in the economy of nature is, chiefly, to be detected by the minute 
analyses, and careful experiments of the chemist. Aeriform* bo- 
dies are vapors, atmospheric air, and gases. Vapors are elastic 
fluids formed from liquid or solid bodies, by means of heat, and 
which, on losing heat, are again condensed into a liquid or a solid 
state. Steam is vapor ; it being nothing more than particles of wa- 
ter, driven to a greater distance by the repulsive power of heat, 
and thus rendered more rare and elastic. The same particles, by 
the loss of heat, may again exist in the form of water, or by los- 

* The term aeriform is from the Greek aer, signifying air or spirit. 

377. Definition of pneumatics. 

378. Gases. Aeriform bodies. Vapors. Are vapors permanently elastic 
fluids ? 



AERIFORM BODIES. 133 

ing still more heat, may become ice. Because steam may thus 
be condensed into a liquid and even a solid form, it is not consid- 
ered as a permanently elastic fluid. 

379. The gases and atmospheric air never exist in either a 
liquid or solid form, except when combined with other substances ; 
nor is it easy, by any ordinary degree of cold or pressure, to 
bring them into these states. They are, therefore, called per- 
manently elastic fluids. 

380. A substance to be elastic must be compressible, and at the same 
time possess the power of expanding to its original bulk when the pressure 

is removed. " Let A B be a cylinder, in which the piston 

rig. 131. p moves, air tight, and suppose that a small portion, as a 

cubic inch of atmospheric air in its common state, be con- 

P tained between the piston and the bottom of the cylin- 

«-— -•- — » der ; suppose the piston now drawn upwards, (as at C.) so 

as to increase the space below it to two cubic inches. — 

A 1. ._ The air will not continue to fill one cubic inch, leaving the 

other cuhic inch unoccupied, as would be the case if a 
solid or liquid had been beneath the piston in the first in- 
stance ; but it will expand, or dilate, until it spreads itself 
through the two cubic inches, so that every part of this 
space, however small, will be found occupied by air. — 
Again, suppose the piston further elevated, ("as at D,) so 
that the space below it shall amount to three cubic 
inches; the air will still further expand, and will spread 
itself through every part of the increased space ; and the 
effect would continue to be produced, to whatever extent 
the space might be increased through which air is at liberty to circulate."* 

381. Atmospheric air is a permanently elastic fluid or gas, 
composed of two kinds of gas, oxygen and nitrogen. The an- 
cients considered common air as a simple element ; but chemical 
malysis has shown its compound nature. 

382. As the mechanical laws and properties of liquids are, in 
hydrostatics, chiefly illustrated by a reference to water as a rep- 
resentative of the whole class of non-elastic fluids, so the me- 
chanical laws and properties of aeriform bodies, or elastic fluids, 
ire exemplified in pneumatics hy a reference to common air. 

283. The solid portion of the globe, being most influenced by 
gravity and cohesive attraction, occupies the lowest place, form- 
ng the great centre of the whole mass. Above this, floating 
within cavities, and filling up the inequalities of the solid sub- 
stances, is the liquid body which constitutes oceans, seas, lakes, 

* Lardner's Treatise on Pneumatics. 

379. Why gases and air are called permanently elastic fluids. 

380. Experiment to show the elasticity of air. 

381. Component parts of common air. 

382. Common air considered as representing the class of aeriform bodies. 

383. Lowest portion of the globe. Substance which fills up the cavities 
if the earth. Substance which envelops the globe. Atmospheric ocean, 
ta use and importance. Analogies between the aqueous and atmospheric 
►ceans. 

12 



134 NATURAL PHILOSOPHY. 

and rivers. A third substance, less influenced by gravity, and not 
affected by cohesion, envelops the whole ; it may be considered an 
atmospheric ocean of nearly fifty miles in depth. In this fluid 
man and animals are fitted to exist, as the aquatic tribes are 
adapted to their watery element ; fresh air being as necessary to 
the former, as water is to the latter. The fish does not die sooner 
when taken out of water, than does the bird or insect which is 
confined in a vessel exhausted of air. The fish swims in the 
water by means of fins, and the bird and the insect fly in the air 
by means of wings. Man, by his muscular strength, treads upon 
the solid earth ; but he moves in an ocean of air, and, every min- 
ute, consumes in respiration, not less than a gallon of this ele- 
ment.* There are plants which grow only when surrounded and 
fed by water, but most of the vegetable tribes require the constant 
agency of air, in order to support their vital functions. Gentle cur- 
rents of water bear upon their smooth surfaces the light bodies 
which float there ; but the torrent hurries onward carrying away 
rocks and embankments, and destroying in a moment the proudest 
works of art. Air, which now gently wafts the floating gossamer, 
when it appears in the terrific form of the whirlwind, uproots the 
oak of the forest, prostrating, alike, the works of nature and of art. 

The Atmosphere. 

384. The Atmosphere which surrounds the globe consists of 
air, with the clouds, and other vapors which float in it. It revolves 
with the earth, around the sun. It reflects the sun's rays upon the 
earth ; but it is proved, that this power of reflection does not ex- 
tend above the height of forty five miles ; therefore, it is supposed 
that the atmosphere does not extend much beyond that height 
above the earth. It is not of equal density in all its parts ; as the 
lower portions sustain the pressure of those above, they are con- 
sequently more dense. The greater the elevation, the lighter or 
more rare is the atmosphere. The air is also colder in propor- 
tion as we ascend into the higher regions ; for it is not heated by 
the rays of the sun which it transmits to the earth, as gaseous 
fluids permit radiant matter to pass freely through them, without 
any absorption. Air receives heat from the earth, and by actual 
contact with such matter as contains it ; that is, the stratum of air 
next the earth receives a portion of heat, which in turn communi- 
cates heat to the air above it, and so on ; the quantity of heat 

* We here use the term element in its popular sense, and not according 
to the laws of science, which confine it to substances that are simple, or not 
capable of decomposition. 

384. Atmosphere, its component parts, revolution and height. Its density. 
Whv flie air near the earth is warmest. 



tiu: A.IR-PUMP. 135 

communicated, decreasing, in proportion as the distance from the 
earth increases. For every 300 feet of elevation, the tempera- 
tun' of the air is found to be one degree lower, or the climate one 
degree colder. 

Air is Material. 

885. Matter is that which is perceived by our senses. We do 
not soo the air which immediately surrounds us, because it is 
transparent; but we feel it in the breeze, and we hear it, in all the 
sounds which fall upon the ear. Its existence is also manifested 
to our senses in a great variety of common appearances, and in 
experiments which may be almost infinitely multiplied. Air, 
though generally considered as visible, is not so ; we do not in- 
deed see it in the apartment where we sit, but when we look 
abroad upon the concave firmament, illuminated by light, we see 
an azure-colored vault. This color is that of the mass of atmos- 
phere, through which we behold the celestial luminaries. The 
distant mountain and the ocean have the same hue, not because 
this is their own color, but that of the medium through which they 
are seen. A small quantity of sea-water scarcely appears color- 
ed, but the deep sea has a decided green color. These phe- 
nomena may be easily explained ; a small portion of sea-water, 
reflects to the eye so little color as not to be perceptible, while 
large masses throw off color in such quantities as to make an im- 
pression upon the eye. 

386. Extension and impenetrability have been stated to be es- 
sential properties of matter. The extension of air is to be per- 
ceived on all sides, we cannot draw a breath without its agency, 
and were we for a few minutes to be deprived of it, suffocation 
and death must ensue. The impenetrability of air, (though this 
may seem at first doubtful,) is not less certain than that of iron 
and wood. No other body can exist in the same space which is 

occupied by air, any more than one solid body 
Fig. 132. can occupy the same space which is filled by 

another solid body. 

387. Plunge a tumbler perpendicularly into a glass 
vessel containing water ; the water will not rise to fill 
the tumbler, because the upward pressure of the fluid 
is resisted by the confined air, which has no chance of 
escape. But if, instead of plunging the tumbler per- 
pendicxilarly, it be held a little inclining to one side, the 
air within will escape in large bubbles, and water will 
rise to fill the inverted tumbler. 

388. Let B A be a glass vessel containing water to 
the level B, and let D C be an empty glass jar, having 

385. Proof that air is material. Air not invisible. 

386. Extension a property of air. 

387. Experiment to prove the impenetrability of air. Exp. 
3:1.!. Experiment 2. 




136 



NATURAL PHILOSOPHY. 




a short tube furnished with a stop- 
cock at F. Let a cork float on the 
surface of the water, at G, and let 
the jar G D, having the stop- cock 
closed, be inverted over the cork G, 
and the mouth, D, be pressed into 
the water in the right-hand vessel 
A B. If the air in C D were capa- 
ble of permitting the entrance of 
another body into the space in which 
it is present, the water in A B, would 
rise in C D, and stand in the same level in the latter vessel as in the former. 
But the water does not enter the inverted vessel, except at a very limited 
height, as will be seen by the cork floating on the surface. The air which 
occupies the space C E excludes the water. This may be proved by open- 
ing the stop-cock F, when the air which opposed the rise of the water will 
escape, and the water, by its upward pressure will ascend to fill the vacant 
space. As air is compressible, the water rises in the vessel C D, to the height 
E, in consequence of the original bulk of the air which filled C D, being re- 
duced by pressure. 

The Air-pump. 

389. One of the most important articles of a philosophical ap- 
paratus, is the air-pump. It shews the effect of the loss of air upon 
animals and vegetables, as under the exhausted receiver, both die. 
By experiments with the air-pump we learn that without air there 
can be no sound, for a bell under the exhausted receiver of an 
air-pump cannot be made to ring — we see that a piece of lead 
and a feather, but for the resistance of the air, would fall in the 
same time from equal heights, or, that both are alike attracted by 
gravity — we see that a very small portion of air in a bladder, ex- 
pands when the pressure of air around it is removed, even to the 
bursting of the bladder which contains it ; — and that a shriveled 
apple under the exhausted receiver, by the expansion of the air 
contained within it, becomes plump and smooth. 

390. Terms used in explaining the construction of the air- 
pump. 

Valve ; — this is merely a little door or lid, which permits a fluid 
to pass in one direction, and prevents its return. On the lower 
board of a common bellows is a large aperture, covered within, by 
a stiff piece of leather, commonly called the clapper. This cov- 
ering, which is moveable on a hinge, is a valve, capable of being 
opened inwardly by the slightest pressure. On raising the upper 
board of the bellows, the cavity within is suddenly enlarged, and 
the valve is opened by the pressure of the external air rushing in 
to fill the vacuum. But the air cannot return by the same aper- 

389. Some of the phenomena exhibited by the air-pump. 

390. Valve. How does the air enter and escape in a common bellows ? 
Valve of the air-pump. Describe the piston and cylinder. Piston-rod. 



THE AIR-PUMP. 



137 



<*** 



ture at which it entered, because it presses upon the valve and 
keeps it closed. On depressing the upper hoard of the bellows, a 
stream of condensed air rushes out at the only opening it can lind, 
viz., the nozle. The reason why an aperture in the leathern sides 
of a bellows destroys its utility is, that the air finding other vent, 
Inues hut feebly through the nozle. 

The valve of the air-pump usually consists of a strip of oiled 
silk, tied over a small orifice. The air pressing outwards, raises 
this valve and escapes. 

Piston and cylinder ; — The piston is a stopper, or moveable plug 
fitted to a hollow cylinder, called a barrel. The piston is moved 
by means of a handle, called the piston-rod. It is covered with 
leather, and oiled, so as to slide up and down the barrel air-tight, 
or without allowing air to pass by its sides. 

391. We have, in the figure, an interior sec- 
tion of an air-pump ; a b are air-tight pistons 
working, each in its cylinder, by means of the 
piston-rods p p ; c is the space under the receiver 
from which air is to be exhausted ; d, a wheel 
and crank which, by turning, alternately raises 
and depresses the pistons ; e, a valve which, 
when the piston b is raised and a vacuum thus 
formed bejow, is forced upwards, and admits air 
from the receiver through the cavity c : this air 
rushes out by opening a valve in the piston b ; f 
is a valve similar to e, and which, when the pis- 
ton a is raised, admits the passage of a portion 
of air from the cavity c ; this air issues out of 
the air-pump by raising the piston-valve at a. 

392. The figure represents 
what is commonly called a 
double-barrel air-pump, hav- 
ing two cylinders or barrels. 
The use of two cylinders is 
to quicken the operation, for 
while the piston of one is ris- 
ing, that of the other is falling. 
Each piston when elevated, by 
the closing of the valve below, 
and the opening of its own 
valve, draws a portion of air 
from the receiver. A A are 
the brass cylinders in which 




Fig. 135. 




391. Interior section of an air-pump. 

392. Operatiou of the air-pump. Darwin's description of the air-pump. 



138 



NATURAL PHILOSOPHY. 



the pistons wont. C C are the toothed piston handles, adapted to cor 
responding teeth in the pinion-wheel. B is the crank by which the 
wheel is turned, and which in its motion alternately raises and de- 
presses each piston. K is the bell-glass receiver fromjvhich the air 
is to be exhausted. D E is the mahogany frame whkM supports the 
whole. At I is a screw, by the turning of which the external air 
is admitted. H is a barometer -gauge connected with the receiver. 
The receiver should be so closely fitted to the brass plate as to 
exclude the entrance of air. 

The philosophic poet, Dr. Darwin, thus describes the operation 
of the air-pump : 

" Now, as in brazen pumps the pistons move, 

The membrane valve sustains the weight above, 
Stroke follows stroke, the gelid vapor falls, 
And misty dew-drops dim the crystal walls ; 
Rare and more rare expands the fluid thin, 
And silence dwells with vacancy within." 

The " vapor" and " dew-drops" alluded to by the poet, are aque- 
ous particles, of which the air usually contains a portion, and 
which are set free by the sudden expansion of the air in the re- 
ceiver, causing a mist on its inner side. The allusion to silence 
refers to the fact, that in " vacancy," or without air, there can be 
no sound. 



LECTURE XXIII. 



THE PROPERTIES OF AIR. 



393. The properties of air, demonstrated by means of the air- 
pump, are weight, elasticity, pressure, and condensation. 



Fig. 136. 



Weight of Air. 

394. Exp. 1st. The air being exhausted from 
the receiver of an air-pump, it will be held fast 
by the pressure of the external air. On turning 
the screw at I, (Fig. 135,) air rushes in, and the 
receiver may be lifted up with ease, because the 
pressure of the air within, balances that of the 
air without. 

Exp. 2d. If a small receiver be placed under 

393. Properties of air demonstrated by the air-pump. 

394. Experiments for proving the weight of air. Exp. 1. Exp. 2. Exp. 
3. Exp. 4. 





ELASTICITY OF AIR. 139 

Fig. 137. a larger, and both be exhausted, the larger re- 

ceiver will be held fast, while the smaller one 
may be easily moved. This is, because the large 
receiver, having no air within, is weighed down 
by the external air, while the small one is free 
from the pressure of air, without and within. 

Exp. 3d. If a glass receiver, open at the top, 
be covered tight with a piece of bladder, and 
then fixed upon the plate of the air-pump and ex- 
hausted of air, the bladder will burst with a loud 
noise. The weight of the air above, which is 
not counteracted by any pressure below, produces this effect. 

Exp. 4th. A bottle uncorked placed within a receiver, and ex- 
hausted of air, will be found to weigh less than when full of air. 
A. wine quart of air is proved to weigh eighteen grains. 

395. The specific gravity of air is about 800 times less than 
hat of water. In explaining the construction and uses of the ba- 
•ometer, we shall have occasion to make some further remarks on 
he weight of air, especially of the whole atmospheric column. 

Elasticity of Air. 

396. Air is perfectly elastic, since, when compressed, it tends 
o restore itself with a force equal to that by which it is compress- 
id. Air is considered as permanently elastic, because no force 
las yet been able to bring it into a liquid or solid form. 

Exp. 1st. A bladder which seems empty, on being closely stop- 
ted at the neck and placed under the receiver of an air-pump, will, 
vhen the receiver is exhausted, expand by the elasticity of the 
mall portion of air within. A very small quantity of air, when 
eleased from external pressure, will expand to an extent which 
ippears almost unlimited ; on letting air into the receiver, the 
)ladder thus distended will shrink up again, and its sides be press- 
id together by the weight of the external air. 

Exp. 2d. Let a bladder with the neck tied, be put into a wood- 
in box, with a weight of several pounds upon the lid, and this box 
>e placed under a receiver ; on exhausting the receiver, the air 
ti the bladder, by its elastic spring, will raise the lid of the box 
vith the weight upon it. 

Ex. 3d. " The effect of air upon the lungs of animals, is ex- 
mplified by a simple instrument called the lungs-glass. This 
onsists of a glass vessel into which is screwed a brass tube, on 
he end of which is tied a bladder containing a small quantity of 

395. Specific gravity of air. 

398. Air perfectly and permanently elastic. Experiments to show the 
lastioity of air. Exp. 1. Exp. 2. Exp. 3. The lungs-glass. Exp. 4. 




140 NATURAL PHILOSOPHY. 

air. When the glass is placed under the receiver, and the action 
of the pump commences, the air within the blad- 
der will issue out at the tube, while that between 
the bladder and the glass, having no way to es- 
cape, will exert its elasticity and shrivel the blad- 
der (as seen in the figure) ; but on re-admitting 
air into the receiver, a portion will enter the blad- 
der and innate it to its former size. The same 
effect is produced upon the lungs of an animal 
when placed under a receiver, and the air ex- 
hausted : the air in the lungs is drawn out, that in 
the cavity of the chest is expanded, the lungs are 
shriveled up, their action ceases, and death is the 
?? certain consequence unless the air be instantly 
admitted into the receiver, in which case the lungs 
are again inflated and the animal breathes." 

Exp. 4th. A fresh egg contains at its large end a bubble of 
air ; if a small hole be made at the opposite end of the egg pla- 
ced under a receiver, upon exhausting the air, the contents of the 
egg will be forced out of the shell by the elastic spring of the 
bubble of air within. 

397. The peculiar, gurgling sound which takes place on de- 
canting liquids, arises from the elastic pressure of the atmosphere, 
which forces air into the interior of the bottle. At first, the bot- 
tle being filled with the liquid, no air can enter, but as soon as a 
portion of the liquid flows off, an empty space is formed within the 
bottle ; a bubble of air, forcing its way through the liquid in the 
neck, rushes to fill its vacuum, and this causes the gurgling sound, 
which will continue, until such a portion of the liquid has passed out 
as will allow the remainder to flow without completely filling the 
neck of the bottle. The report which accompanies the uncorking 
of certain liquors, is owing to the elastic force of the air which 
was condensed within the bottle. When liquor is bottled, a 
small space left near the top of the bottle is filled with air ; on 
driving in the cork, this air is condensed, the same quantity 
being made to Occupy as much less space as the cork fills. 
The nature of some liquids is to produce, when bottled, a quan- 
tity of gas, and this often presses with such force as to drive out 
the cork, or, if this is secured, to burst the bottle. The froth 
which appears on pouring out bottled beer or porter, the efferves- 
cence of soda water, the sparkling of cider and champaigne wine, 
&c. are owing to the pressure of condensed air, which appears in 
the form of little bubbles. 

397. Cause of the sound in decanting liquids, uncorking bottles of beer, 
&c. Frothing, effervescence, and sparkling of liquors. 



PRESSURE OF THE AIR. 



141 



Fig. 139. 




l'ressure of the Air. 

398. From the weight and elastic//// of the air, arises its pre*. 
rare; and experiments which prove the two former properties, 
jquallj demonstrate the latter. But for the sake of" greater clear- 
iMfls, we prefer to consider these analogous properties under dis- 
tinct heads. 

399. If, as has been ascertained, one quart of air weighs eigh- 
teen grains, the weight of a column of air, extending nearly fifty 
miles above us, must be very great ; and, consequently, its pres- 
sure, which is in proportion to its height, must also be great, If 
ithe human body was subjected to the pressure of a column of air 
directly over it, without any counteracting pressure from within 
and around, the incumbent weight would be insupportable. 

400. Let a glass having an opening at the top, be 
placed over the plate of the air-pump, and let a 
person lay his open hand upon the top of the vessel 
so as to cover it closely ; on turning the handle of the 
air-pump a few times, the hand will be pressed 
down with such force as to render it impossible to 
raise it, and much pain will be felt. The pressure 
under the hand being removed, by exhausting the air from within 
the glass, the pressure from above is thus left to operate without 
any counteracting force. The pain which is experienced will 
serve to show, in some degree, what would be the effect upon the 
whole body, if all but the downward pressure were removed. 

401. The actual amount of pressure of a column of air upon 
every square inch, is demonstrated by an experiment with a sim- 
ple apparatus called the Magdeburgh hemispheres.* 
This consists of two hollow hemispheres of brass, A 
B, made to fit so closely as to form an air-tight globe. 
In the lower part, C, is a stop-cock E, and a tube 
which screws into the plate of the air-pump ; when 
the air is exhausted within the globe, the stop-cock 
being turned to prevent the return of the air, the ap- 
paratus may be taken from the air-pump, and the 
handle C screwed on to the tube. Before the' air 
was exhausted from the interior of the globe, the two 
parts could be separated with ease, but when subjected 
only to external pressure, they adhere with much 
force. Under an exhausted receiver, the hemispheres 

This experiment was one of the first which drew the attention of man- 

What causes the pressure of air ? 

How can the human body endure the downward pressure of the 

Experiment for proving the pressure of air. 
Experiment with the Magdeburgh hemispheres. 



Fig. 140. 




398. 
399. 
air? 
400. 
401. 



142 



NATURAL PHILOSOPHY. 



Fig. 141. 




Fig. 



142. 



thus exhausted, may easily be separated, because the exter- 
nal, as well as the internal pressure of air is removed. By 

means of a steelyard hooked to a 
ring at the top of the globe, it may 
be proved what weight is necces- 
sary to overcome this pressure of 
the atmosphere ; for when the 
weight, W, is at a certain point on 
the arm of the steelyard, the upper 
hemisphere is lifted up. Suppose 
the mouth of the hemisphere con- 
tains 12 square inches, and that it 
requires a weight of 180 pounds to 
raise the upper one ; if we divide 
the weight 180, by 12, the number of inches, the quotient is 15 
pounds, which is the pressure on every square inch of surface. — 
That is, a column of air reaching to the top of the atmosphere, 
and whose base is a square inch, weighs 15 pounds. 

402. The figure represents a square inch ; 
the inclosed space must therefore sustain 
the pressure of fifteen pounds. Every per- 
son must then sustain a pressure of air 
equal to 15 times as many pounds as there 
are square inches on the surface of that 
body. Suppose the surface of a man's 
body to measure 2000 square inches, the 
force of the atmosphere pressing on that 
surface would be equal to 30,000 pounds. 
But the air being so uniformly distributed, 
within, without, and on all sides, we are 
not sensible of this pressure. 

403. Boys, sometimes in their sports, and without knowing it, make philo- 
sophical experiments ; thus the leather-sucker illustrates the pressure of air, 
arising from the joint effect of elasticity and weight. This is nothing more 
than a piece of leather having a cord attached to its center. On moistening 
this, and applying its surface to any heavy body, as a stone or block of wood, 
it will adhere so firmly that the body may be raised by the string. This 

kind to the mechanical properties of air. The inventor of the apparatus was 
Otto de Guericke, of Magdeburgh in Germany, who had hemispheres made 
of a foot in diameter. It is said that at a public exhibition of his apparatus, 
six horses of the emperor were unable to pull the hemisphere asunder. 
There being no air-pump at this period, (about 1657,) the inventor was 
obliged to exhaust the hemispheres of air, by the slow process of filling them 
with water, and then extracting the water by means of an exhausting syringe, 
or common pump, applied at the tube. 



402. Pressure on one inch of surface. Amount of pressure on the human body . 

403. The leather-sucker. Flies walking on ceilings and window-panes. 



PROPERTIES OF AIR. 



143 



Fig. 143. 




effect arist's from the exclusion of the air between 
the leather and the stone. The air pressing with 
a weight of nearly fifteen pounds upon a square 
inch, it follows that witn a square inch of leather 
a stone of nearly fifteen pounds weight may he 
raised. 

The power of flies and some other insects, to 
walk on smooth ceilings with the feet upwards, or 
upon perpendicular panes of glass, depends on the 
same principle as the action of the sucker. Their 
feet are so constructed as to be capable of exhaust- 
ing the air under their soles. There is an animal 
of the lizard kind which can thus walk with its 
back downwards, and the walrus and seal walk on walls of smooth ice. 

404. " Breathing is, in part, the effect of the pressure and 
elasticity of air. When we draw in the breath, we first make an 
enlarged space in the chest. The pressure of the external at- 
mosphere then forces air into this space so as to fill it. By mus- 
cular action, the lungs are next compressed, so as to give to this air 
a greater elasticity than is allowed by the pressure of the external 
atmosphere. By the force of this elasticity, air is propelled, and es- 
capes by the mouth and nose. It is obvious, therefore, that the air 
enters the lungs, not by any direct act of these organs upon it, but 
by the weight of the atmosphere forcing it into an empty space, 
and that it is expired by the action of the lun^L conpressing it. — 
The action of the common bellows is precflBly similar, except 
that the aperture at which the air is drawn in, is different from that 
at which it is expelled."* 

405. The figure represents an ink-bottle constructed upon the 
principle of atmospheric pressure. It is evi- 
dent that were the top at A open, the liquid 
would flow out at the tube C, until that in the 
body A B were brought to the level of C. — 
But the body is entirely close, while the tube 
C is open. The bottle is filled, by being 
placed in an inclined position and pouring in 
ink at C. Let the bottle now be placed up- 
right as in the figure, and the pressure of the 

atmosphere at the orifice C, will prevent the liquid from run- 
ning out. We now perceive why it is necessary to make an open- 
ing, called a vent-hole, at the top of a cask, that the liquor within 
may flow out at an orifice at the side or bottom. The pressure of 
the external air acting upon the liquor at the orifice would prevent 



Fig. 144. 




(W 



* Lardner's Treatise on Pneumatics. 



404. What effect has air upon breathing ? 

405. Scientific ink-bottle. Why are casks and tea-pots furnished with a 
vent-hole ? Fountain lamp. 



144 



NATURAL PHILOSOPHY. 



Fig. 145. 



its flowing out, unless this pressure were counterbalanced by at- 
mospheric pressure within the cask, in which case the liquor de- 
scends by its own weight. A small hole in the top of a tea-kettle 
would prevent the water, when boiling, from running out at the 
spout. It is common for house-wives when the " tea-kettle" boils, 
to raise the lid a little on the side, which has the same effect. — 

Tea and coffee pots when closed 
tight, will not admit liquids to pass 
freely out at their spouts, unless the 
vent hole is made in the side. 

The influence of atmospheric 
pressure in restraining the flow of 
a liquid, is also seen in the argand 
or fountain lamp, where the oil is 
in a part of the lamp A, higher 
than the flame B. The top A be- 
ing filled with oil, is screwed upon 
the body of the lamp, at C. The 
oil descending and passing through 
the horizontal tube which connects 
B to C, rises into the wick and 
thus supplies the flame, while it is 
restrained from flowing out by the 
pressure of the air upon the open- 
ing at the chimney. 

406. The pressure of air is as 
the depth. As the bottom of a 
lake or sea supports the whole 
mass of water above it, so the 
part of the atmosphere next the earth supports the whole mass of 
air. The lower portions of the air sustaining the pressure of 
those above, are, therefore, more dense. Air upon high mountains 
is, for the same reason, lighter than in lower situations. 




LECTURE XXIV. 

THE CONDENSATION OF AIR. CONDENSING SYRINGE. ARTIFI- 
CIAL FOUNTAINS. AIR-GUN. DIVING-BELL. 

The Condensation of Air. 

407. Air from its elastic properties may be greatly condensed, 
or forced by pressure into a smaller space than that which it natu- 



406. Pressure of air proportioned to its depth. 

407. To what is the elasticity of condensed air equal 1 



K)M) i:\8ATION OF AIR. 



145 



rally occupies. The elasticity of condensed air is equal to the 

force which compresses it. 

408. The condenser is a machine which exhibits the proper- 
ties of condensed air. 
At A is a brass barrel 
containing a piston, with 
a valve opening down- 
ivards. On raising the 
handle (a) of the pis- 
ton, the air presses 
through the valve, and is 
forced into a tube com- 
municating with the re- 
ceiver B, which in or- 
der to sustain the inter- 
nal pressure, must be 
made of very thick and 
strong glass. At every 
stroke of the piston, 
more air is thrown in- 
l^ to the receiver. This 
is held down upon the 
W plate C, by the cross 
piece D, and by the 
screws F E. By turn- 
ing the stop-cock G, the 

condensed air is suffered to escape. 

409. The operation of this machine is the reverse of that of 
the air-pump ; in working the latter, we pump air out of the re- 
ceiver, in the former, we press air in. In the use of the air- 
pump, we cause air to expand and become more rare, in that of 
the condenser we continually add to its density. The receiver of 
a condenser may be compared to that of a wool-sack, at first 
filled with wool lying loosely, as in its natural state, and then 
crowded with successive portions, until it is made to contain a 
weight many times greater than at first. But compressible as 
wool is, it is far less so than air, which can be lessened in bulk, to 
a degree to which no limits can be assigned, but the want of strength 
in the apparatus used, and of force in the power applied. 

410. A bell emits a much heavier sound when rung in conden- 
sed, than in common air. 




408. Condenser. 

409. Comparison between the air-pump and condenser. To what may 
the receiver of a condenser be compared ? 

410. What effect has condensed air upon sound? How may a bottle be 
broken by condensed air ? 



146 



NATURAL PHILOSOPHY, 



Fig. 147. 



A thin bottle containing common air and closely corked, will 
be broken inwards, by the pressure of condensed air. 

411. The elastic power of condensed air may be shown in the 
production of artificial fountains. Let a strong vessel of brass 

or copper be furnished with the stop-cock in- 
serted at the top, from which a tube proceeds 
nearly to the bottom. Let the vessel be partly 
filled with water, and with a condensing syringe 
fitted to the upper part of the tube, introduce an 
extra quantity of air into the vessel. As soon 
as a stop-cock is turned, the condensed air act- 
ing on the water beneath, forces it through a 
tube which is inserted in the lower part of the 
vessel, and thus produces a beautiful jet d'eau* 
The greater the quantity of air condensed within 
this fountain, the greater will be the height to 
which the water is forced, because the elastic 
power of air, is in proportion to the force which 
compresses it. If a vessel of similar construc- 
tion to that represented in the figure, and contain- 
ing common air, be placed under the tall receiver 
of an air-pump, when the surrounding air is 

rarefied, the jet will rise, the same as in the case of condensing 

the air within. 

The Geysers of Iceland are spouting springs, occasioned by 

the force of confined air, or gas, acting upon the water; this force 

is immense, since not only water, but large stones are thrown by it 

to the height of more than two hundred feet. 

412. The air-gun affords a striking proof of the force of con- 
densed air. This, in its general appearance, is very like a corn- 
Fig. 148. 





mon gun, with the addition of a metallic ball, A ; into this ball, 
which is furnished with a valve opening inwards, the air is forced 
by means of a condensing syringe, after which the ball is screwed 
on to the gun, below the lock, as appears in the figure. The gun 

* A French phrase signifying an upward spout of water. 

411. Artificial fountains. The Geysers. 

412. Air-gun. 



CONDENSATION OF AIR. 



147 



Fig. 149. 



is now loaded with a bullet, and the lock being sprung, acts upon 
a pin which opens a valve ; the condensed air now rushes into the 
barrel of the gun, and by its sudden expansion, forces out the bullet. 
413. The diving-bell exhibits an interesting illustration of the 
compressibility, elasticity, and impenetrability of air. 

The diving-bell, is a large, open mouthed vessel, capable of 
containing one or more persons. By means of this machine, men 
are able to descend to considerable depths in the ocean, for the 
purpose of saving valuables from the wrecks of vessels, and of 
pursuing works of submarine architecture, such as laying the 

foundation for harbors and light- 
houses. The diving-bell is also 
used in pearl, and coral fishe- 
ries. 

414. When first introduced in- 
to use, it was made of copper, and 
constructed in the form of a bell, 
the height being about eight feet, 
the diameter of the bottom five 
feet, and that of the top three feet ; 
it contained about eight hogsheads. 
Light was admitted by strong 
spherical glasses, at the top, as in 
the cabins of vessels. An En- 
glish poet before the invention of 
the diving-bell, prophetically ex- 
claimed ; — 

Lo ! Britain's sons shall guide 




Huge sea-balloons beneath the tossing tide ; 
The diving castles, roof'd with spheric glass, 
Ribb'd with strong oak, and barr'd with bolts and brass." 

415. When the diving-bell is first let down into the water, it is 
full of air, but the pressure of the surrounding water, (which pres- 
sure increases with the depth,) acting upon the inclosed elastic air, 
compresses its bulk, and the liquid rises proportionally in the bell. 

As a column of water 34 feet deep, causes a pressure equal to 
a whole column of the atmosphere, it follows that at this depth, 
the air in the bell is under a pressure equal to two atmos- 
pheres, viz., that of the whole atmospheric column ; and the 



413. What properties of air are illustrated by the diving-bell ? Why does 
not water completely fill the diving-bell ? The uses of the diving-bell. 

414. Explain the construction of the diving-bell. What condenses the air 
in the bell '? 

415. Pressure at the depth of thirty-four feet. When is the air in the bell 
twice as dense as common air ? What renders the air in the bell impure ? 
How is the impure air let off? How is the diver supplied with fresh air ? 



148 



NATURAL PHILOSOPHY. 



Fig. 150. 



column of thirty-four feet of water ; the air is, therefore, here 
condensed into half its original bulk because a weight of two at- 
mospheres is found to diminish the bulk of air to one half, of three 
atmospheres to one third, or of fifty atmospheres, to one fifteenth 
of its former bulk. As the depth of the water, and consequently 
the pressure increases, the air will be proportionally condensed, 
and the water will rise in the bell. When the air is twice as 
dense as air at the surface of the earth, the diver at each inspira- 
tion of the breath, will receive twice as much air into the lungs 
as when breathing common air. 

In breathing, the diver is constantly throwing from his lungs a 
large portion of a gas, which is fatal to animal life.* This impure 
air being more rarefied than the air within the bell, rises, and is 
let off by opening a stop-cock at the top of the machine. In or- 
der to supply the diver with fresh air, barrels of air having leaden 
weights attached to them, are let down, (see c, Fig. 149,) and by 
means of connecting tubes they convey air into the bell. At 
e is a man walking at a little distance from the bell, to recover 
some bales of goods which had been thrown overboard from a 
vessel in distress. He wears on his head a leaden cap, having 
glasses in front to admit light, and breathes 
by means of air from the flexible tube con- 
nected with the bell. In this manner, the 
divers sometimes go a hundred yards from 
their bell. 

The bell is furnished with seats for the 
workmen, and with tools of various kinds. 
416. A machine of later construction, is 
considered an improvement upon the diving 
bell, a, (Fig. 150,) is a bent tube connected 
with a forcing air-pump, d, by means of which 
a constant supply of fresh air is sent down 
from a ship above; this air. the diver can 
obtain by turning the stop-cock. At the 
bottom, are heavy balls of lead, to sink the 
machine vertically. Men in the ship above, 
raise the machine by means of ropes and 
fixed pulleys. When the divers wish to be 
drawn up, they pull a rope which rings a 
bell ; when they want to convey information 
to those above, they write upon a sheet of 
lead which they send up, by pulling a cord 
moving over a pulley fixed to the ship. 

* Carbonic acid gas. 




416. Describe the diving-bell represented in Figure 149. 



BAROMETER. 149 

LECTURE XXV. 

BAROMETER. EFFECT OF HEAT UPON AIR. 

417. The ancients had no conception that the pressure of air 
caused it to penetrate every crevice and cavity on the surface of 
the earth ; they said, therefore, it was because nature abhorred a 
vacuum, that where there was nothing else, there was sure to be 
air. They perceived that when a solid or liquid was removed, 
the surrounding air immediately rushed in to take its place ; but 
instead of referring this fact to the simple and obvious principle of 
atmospheric pressure, they seemed resolutely to shut their eyes to 
the light of truth, and rested satisfied with their absurd hypothesis, 
that nature abhorred a vacuum. The effect of suction with the 
mouth, is, probably, one of the first ways in which the subject of 
atmospheric pressure forced itself upon the observation of man- 
kind. When one end of a tube is immersed in a liquid, and the 
other placed in the mouth, the air may be withdrawn from this tube 
by inhaling, and water will rush into the tube as fast as the air 
leaves it. Ancient philosophers could not see in this, any evidence 
of atmospheric pressure, but, like children, who attempt to account 
for what they do not understand, they said, " we suppose this takes 
place because nature being uneasy with a vacuum, makes the wa- 
ter rise to fill it." This kind of reasoning, though fatal to the 
progress of true physical science, did not prevent men from con- 
structing common pumps of various kinds, in such a manner 
that they answered the desired purposes. About two hundred 
years ago, as some engineers of the Grand Duke of Florence at- 
tempted to raise water, by means of a common pump, to the height 
of fifty or sixty feet, they perceived that the water, after mounting 
about thirty-four feet, would rise no higher. They communicated 
this fact to Galileo, the most celebrated philosopher of that day. 
After various experiments, he became satisfied that this was a uni- 
versal law of nature, and that the rise of water to a certain height 
in pumps exhausted of air, was neither owing to nature's horror of 
a vacuum, nor to the power of suction, (as some had vaguely sug- 
gested,) but to atmospheric pressure. 

418. Torricelli, a pupil of Galileo, carried his inquiries farther. 
As a column of thirty-four feet of water is equivalent to a column 

417. Ignorance of the ancients respecting atmospheric pressure. Their 
hypothesis Attempts to raise water in pumps more than thirty-four feet. 
Discovery of Galileo. 

418. Torricelli's experiments. What column of water and what of quick- 
silver, are equal in weight to a column of the atmosphere ? 

13* 



150 



NATUEAL PHILOSOPHY. 



of air extending upward from the surface of the earth through 
the whole region of the atmosphere, why, he inquired, may not 
a column of any other fluid, of a given height, balance a column 
of air? As quicksilver is nearly fourteen times heavier than wa- 
ter, he imagined that a column of that fluid, of one fourteenth part 
the height of a column of water thirty-four feet high, might be 
equal to the pressure of air. He therefore filled with quicksilver, 
a glass tube, A B, of about three feet in length, closed 
Fig. 151. at one end, and open at the other, and placing the open 
end of the tube in a basin of quicksilver, C, he found that 
the fluid in the tube fell a little, but remained suspend- 
ed at about 20 or 30 inches, leaving a space at the top 
of the tube, above the quicksilver, which was a perfect 
vacuum. By dividing 34 feet, (408 inches,) the height 
of water which the pressure of the atmosphere will 
support, by 14, (because quicksilver is 14 times heavier 
than water,) the quotient 29, shows that a column of 
quicksilver of the height of 29 inches, equals in weight 
a column of water of 34 feet. 

419. But even after the experiments of Torricelli, 
though it was admitted that the quicksilver was suspended in the 
tube by the pressure of the surrounding air, it was not observed 
that the height of the column of quicksilver was not always the 
same ; or, in other w 7 ords, the fact was not yet known, that the 
pressure of the air was, sometimes, greater than at others. But as 
Torricelii's tube excited the attention of men of science, it was 
soon discovered that the quicksilver did not always stand at the 
same height ; and, moreover, that its rising, or falling, was usually 
accompanied, or followed, by a change of weather. The quick- 
silver being found to vary from about 27 to 31 inches, a gradua- 
ted scale was affixed to the tube, divided into inches and tenths 
of an inch, in order to show, with accuracy, these variations ; this 
instrument was called the weather-glass, and, afterwards, received 
the more scientific name of barometer. 

420. The word barometer, is from two Greek words, baros, 
weight, and metron, measure, signifying to weigh the atmosphere. 
Let a tube, A, of nearly three feet in length, closed at one end and 
open at the other, be filled with quicksilver and inverted in a 




419. What fact respecting atmospheric pressure was still unobserved ? 
How was the variation in atmospheric pressure discovered ? The weather- 
glass. 

420. Meaning of the word barometer. Construction of the barometer. 
Why does not the quicksilver in the tube of the barometer run into the cup ? 
What proves that the column of quicksilver in the barometer has the same 
weight as a column of air? 



BAROMETER. 



151 



Fig. 152. 



Fail' 
Ckttng* . 
Ji-tt in \ 



3/ 

fiHO 
20 

§28 
27 



cup, B, also containing quicksilver. If the tube were open 
at the top, (according to the law that all fluids seek an equi- 
librium,) the quicksilver from the tube, would de- 
scend to a level with that in the cup. But at the 
top of the column of" quicksilver there is no pres- 
sure, because, when the tube was filled with this 
fluid, all the air was excluded, and when on in- 
verting the tube, a space was left at the top by 
the descending of the quicksilver, this space was 
a perfect vacuum, and, therefore, all downward 
pressure upon the column of fluid in the tube is 
removed. But the air presses upon the quick- 
silver in the cup, and this forces the fluid up- 
wards, or which is the same thing, supports it 
thus suspended, with the open end of the tube 
immersed in the contents of the cup. And this 
column of quicksilver must have the same weight 
as a column of the atmosphere of the same base, 
or it would not be thus balanced by it. As the 
variations in the barometer correspond to the va- 
riations in the w r eight of the air at a given 
place, this instrument becomes a weatlier-glass, 
indicating changes in the weather. The rise of 
the barometer denotes fair weather, its fall de- 
notes stormy weather. A violent wind is often 
preceded by a very sudden and great descent of 
the mercury. 

421. Barometers are sometimes made with the 
lower end of the tube bent, (as in Fig. 153,) and 
terminating in a small open cup containing mercury. 
The principle of their construction and operation, is 
the same as in the barometer with the straight 
tube. 

422. In describing the air-pump, we remarked 
that with it, was usually connected a part called the 
barometer-gauge. The object of this is to measure 
the degree to which the air is rarefied. When 
the exhaustion of the air, in the receiver, commences, 
the quicksilver of the barometer falls, because the 
air which supports it is lighter. If it fall a thousand 
degrees below where it stood before the action of 
the air-pump began, the air in the receiver is said 
to be rarefied 1000 times. 




153. 




421. What does the variation in the barometer prove 1 

422. Barometer-gauge connected with the air-pump. 



152 NATURAL PHILOSOPHY. 

Uses of the Barometer. 

423. 1st. The barometer enables us to determine the exact 
weight of a column of atmospheric air, since this is equal to the 
weight of a cylinder of quicksilver, thirty inches in length. 

424. 2d. The barometer is used for the purposes of determin- 
ing the height of mountains, ascent of balloons &c. ; as atmos- 
pheric pressure is less in proportion to elevation, the barometer 
falls in the same ratio. It is a common rule, that the barometer 
falls 1 inch for 1000 feet of elevation. Thus, in ascending a 
mountain, we should infer from the fall of the quicksilver ^ an inch, 
that we were 500 hundred feet above the level of the sea. Upon 
the summit of Mont Blanc, an elevation of 15,000 feet, the baro- 
meter falls about 15 inches. 

425. 3d. The barometer is of great use to the mariner, who in 
unknown climates, is often able, by its variations, to foresee and 
prepare for sudden changes of weather. " The watchful captain 
of the present day, trusting to this extraordinary monitor, is fre- 
quently enabled to take in sail, and to make ready for the storm, 
when in former times, the dreadful visitation would have fallen 
upon him unawares."* 

426. 4th. The sudden fall of the mercury in the barometer, 
generally denotes rain or wind, or what we call bad weather. — 
Though, in such weather, we complain of the heaviness of the 
air, it is, in fact, its lightness that causes the feelings of dullness 
and oppression which we experience. For at each inspiration 
of the breath, we take in less air when it is rarefied than when 
it is more dense ; on the contrary, the man in the diving-bell at 
the depth of thirty-four feet of water, where the pressure is that 
of two atmospheres, breathes air of twice the usual density. — 
When the air is more light or rare than usual, the damp vapors 
and unhealthy gases, which, supported by pressure from below, 
floated in higher regions, now descend, towards the earth. These 
vapors and gases have an unfavorable influence on the human 
system, obstructing perspiration, the free play of the lungs, and 
the circulation of the blood, and in this way giving rise to diseases 
of various kinds. When therefore we see fog hanging over the 
surface of the earth, and smoke falling instead of rising, we may 

* Arnott. 

423. Height, of the atmospheric column determined hy the barometer. 

424. Effect of elevation upon the barometer. 

425. Use of the barometer to the mariner. 

426. What is indicated by the sudden fall of the barometer ? Air lighter 
in bad weather. Effect of a light atmosphere upon the human system. 



BAROMETER. 153 

infer that the surrounding air is lighter than when fog and smoke 
rise into higher regions of the atmosphere. 

427. As the falling of the barometer denotes bad weather, so 
its rising announces fair weather, though these indications are 
not always to be depended on, especially when the variations in 
the height of the mercury are slow and inconsiderable. It is 
stated by English writers, that, on the occasion of the great Lis- 
bon earthquake, the barometer, even at the distance of Great 
Britain, fell five or six inches ; a phenomenon which is scarcely 
eve? observed to take place, at the surface of the earth, under any 
circumstances. 

428. The mean pressure of the atmosphere at the level of the 
sea, is proved to be nearly the same in all parts of the earth. — 
The mean height of the mercury in the barometer has been found 
to be above 30 inches, in various places in the torrid, temperate 
and frigid zones. 

429. In making accurate observations with the barometer, it 
is necessary to have attached to this instrument a thermometer , 
with a scale of correction to show how much to add or subtract 
from the height of the mercury, on account of changes of the tem- 
perature. The mercury being made lighter by heat, will rise in 
the barometer tube, when no change has taken place in the pres- 
sure of the air. The thermometer shows, exactly, the degree of 
this expansion of the mercury by heat, and therefore what must 
be subtracted from the height of the barometer, in calculating 
upon the weight and pressure of the atmosphere. On the con- 
trary, in cold weather, the mercury is heavier, and consequently 
w r ill stand lower in the barometer, although the pressure of the 
air may be the same ; something therefore must then be added to 
the report of the barometer. At the equator Ave should have to 
subtract from the height of the barometer, while in the frigid 
zone we should add to it ; and this according to the degrees of 
temperature indicated by the thermometer. 

Effect of Heat upon Air. 

430. Heat, which so much affects solids and liquids, has a 
powerful influence upon air. Of this we are continually remind- 
ed by the changes of temperature around us ; thus we say, the air 

427. What is indicated by the rising of the barometer? Fall of the ba- 
rometer at the time of the Lisbon earthquake. 

428. Mean pressure of the atmosphere at the level of the sea. 

429. Use of connecting the thermometer with the barometer. Effect of 
temperature upon the barometer. 

430. Causes of variations in the temperature of the air. Effect of heat 
upon air. 



154 NATURAL PHILOSOPHY. 

is chilly, warm, cold, &c. But as the moisture or dryness, the still- 
ness or motion of the air, all conduce to these variations of tem- 
perature, we are not to attribute them to heat, only. Heat expands 
air, and thus rarefies, or makes it lighter. Let a bladder, tied at 
the neck, and containing a small quantity of air, be held near the 
fire, the sides will soon begin to be pressed out by the expansion 
of the air within. On removing the bladder to a colder place, the 
air will condense, and its sides collapse as before. 

431. The balloons first used were filled with hot air, which, be- 
ing lighter than the atmosphere around, arose, and floated in it. 
Dr. Arnott says, " the first balloon was constructed by a man igno- 
rant of what he was really effecting. Seeing the clouds float high 
in the atmosphere, he thought that if he could make a cloud, and 
inclose it in a bag, it might rise and carry him with it. Then erro- 
neously deeming smoke and a cloud the same substance, he made 
a fire of green wood, wool, &c, and placed a great bag over it, 
with the mouth downwards to receive the smoke. He soon had 
the joy to see the bag full, and ascending ; but he understood not 
that the cause was the hot and dilated air within, which being 
lighter than the surrounding air, was buoyed up, while the visible 
part of the smoke, which chiefly engaged his attention, was really 
heavier than the air, and was an impediment to his wishes." — 
Montgolfier, of France, may be considered as the inventor of the 
air-balloon. To an elliptical bag of silk, 74 feet in length, and 48 
in breadth, he attached a car for aerial travelers ; and succeeded 
in raising this immense balloon by means of air, heated by burning 
combustibles in a grate, below the silk bag. The discovery of the 
properties of hydrogen gas, soon caused that substance to be substi- 
tuted for heated air, in inflating balloons. 

Smoke. 

432. The ascent of smoke, is caused hy the air becoming 
lighter by heat. Smoke consists of the vapor, gases and dust, 
which arise from burning fuel, and is borne upward by the rising 
current of heated air, in the same manner as straws and other 
light substances are carried along by a stream of water. All that 
is visible in smoke is really heavier than air, and soon falls, set- 
tling upon the sides of chimneys, or the roofs of houses, and sur- 
rounding objects, in the form of soot or fine powder. As hot air 
is continually rising in a heated chimney, its place is supplied by 



431. First attempt to construct a balloon. Inventors of the air-balloon. 

432. Why smoke ascends. What smoke consists of. Is smoke lighter 
• than air? Process which goes on in a heated chimney. The chimney does 

not draw smoke. 



WINDS. 155 

colder air, which moves in all directions toward the fire place, to 
fill the void. This colder air, being, in turn, heated, rises also in 
the chimney, which is thus iilled with a column of air much lighter 
than a column of atmosphere of the same height, and therefore 
issues from the top of the chimney, being forced up by the colder 
and denser air which rushes in at the fire-place. We perceive 
therefore, that to say the chimney draws smoke is not strictly ac- 
curate, since it is the current of heated air which bears the smoke 
upward. We may now understand why a door or window should 
be opened to free an apartment from smoke ; — a current of fresh 
air being thus thrown in, not only promotes the combustion of 
fuel, but, by its pressure, impels the lighter air of the chimney 
upwards. 



LECTURE XXVI. 

WINDS. THEIR CAUSES AND EFFECTS. 

433. Wind is air in motion. Currents of air are caused by 
variations of temperature. When any part of the atmosphere is 
more heated than the surrounding air, it becomes lighter, and 
rises, while the heavier air rushes in to supply its place ; and this, 
in turn, becomes heated, and ascends, and thus a current of air is 
produced which is always in the direction toward the greatest heat. 
There is a rush of air from open doors or windows towards the 
heated fire-place of a room. Ifj when the air is calm, a fire be 
made of straw or other light combustibles in an open field, cur- 
rents of wind will begin to flow towards the fire. During the con- 
flagration of a building, the same fact will be strikingly manifested, 
for as the heat, and consequently the rarefaction of the air becomes 
greater, the force of the currents rushing to take the place of the 
ascending air, is consequently greater. 

434. The sun being the great source of heat to the earth, its 
situation must, of course, greatly influence the direction of winds. 
If the earth did not revolve on its axis, one portion of its surface 
being then continually more exposed to the rays of the sun, the 
air would be here the most rarefied and ascend into higher regions, 
like smoke from a great fire, while, towards this point, would be 

433. Causes of currents of air. Why does the wind blow towards a fire ? 

434. Cause of the constant east winds at the equator. Where are the 
winds most violent? 



156 NATURAL PHILOSOPHY. 

impelled the surrounding colder, and heavier air. But as the 
earth does revolve on its axis, it follows, that successive portions 
of its surface are presented to the sun, and become heated ; now 
as the heated part is constantly moving eastward because the 
earth revolves from west to east, and carrying in that direction 
the rarefied air, there is generally a current blowing in this direc- 
tion, or a constant east wind at the equator. The equatorial re- 
gion being that part of the earth which is most heated, the equili- 
brium of the air is here most disturbed, and winds most violent 
and terrific. 

435. The laws of mechanics with respect to the motion which 
results from the composition of two or more forces, influence the 
action of the winds, no less than of solid, moving bodies. The 
direction of the wind may depend on various causes, being the 
resultant of two or more currents, or forces. As we go from the 
equator to about the 30th degree of latitude, the wind is found to 
vary from the east point, so as to become north-east on the north- 
ern side, and south-east on the southern side of the equator. — 
This is because the equatorial parts being hotter than any other 
on the globe, the currents of less rarefied air from the north and 
south move that way, but the northern current meeting with the 
eastern, or that which follows the diurnal motion of the earth, the 
resultant is the north-eastern wind ; while the southern current 
also falling in with the eastern, produces, by the composition of 
the two forces, a south-east wind. These constant winds which 
always blow nearly in the same direction, from their great im- 
portance for navigation and commerce, are called trade-winds. — 
They prevail mostly in the Pacific and Atlantic oceans, and in the 
seas connected with them. 

436. Currents of air also, in the seas between Asia and the equa- 
tor, produce the monsoons, or shifting trade-winds. These differ from 
the constant trade-winds, because they change their course every 
half year, when the sun changes its position from the northern to the 
southern side of the equator; that is from March to September, 
or when the sun is north of the equator, the monsoons blow from 
the south-west ; while the remaining part of the year, or when 
the sun is south of the equator, they blow from the north-east.— 
About the period of the equinoctial changes, there is a change in 
Aese winds, or, as the sailors term it, " a breaking up of the mon- 
soons ;" the seas where they prevail, are then subject to storms, 
hurricanes, and dead calms. The Indian ocean is most affected 
by these winds. When the sun is north of the equator, the sur- 

435. Motions of the wiud governed by mechanical laws. Variations of 
wind as we go from the equator. Trade winds, how formed ? 

436. Monsoons. Breaking up of the monsoons. Why the Indian oceaQ 
h most affected by them. 



WINDS. 157 

rounding Asiatic coast, being exposed to its direct rays, is hotter 
than the Indian ocean, and the wind blows from the ocean to- 
wards the coast ; when the sun is south of the equator, the ocean 
being more heated, the wind blows towards it from the coast. 
Navigators to China and the East Indies, are, therefore, obliged to 
pay much attention to these winds. 

437. Land and sea breezes are periodical winds which change 
their direction every day ; they are chiefly confined to tropical 
regions, where the wind blows towards the coast during the day, 
and towards the sea during the night. The land reflects the rays 
of the sun more powerfully than the water ; therefore, during the 
day, the air over the land is more rarefied than that over the 
water, and rises into higher regions of the atmosphere, while the 
surrounding cooler and denser air rushes in to fill the void. As 
soon as the hot sun darts his scorching beams upon the islands 
and coasts of the torid zone, the refreshing sea breeze comes to 
revive with its balmy breath the parching land and fainting in- 
habitants. 

Who, in contemplating the beautiful provisions of nature, can 
doubt, that nature, herself, is under the control of a wise and good 
Director ! How many facts of science reveal to us that the whole 
creation is but a chain of infinite and harmonious relations, the 
one depending upon and influencing the other, and all upheld by 
one governing and changless mind ! And how often in the moral 
government of God, do peace and consolation, like the sea breeze 
which is produced by the scorching rays of the sun, accompany 
the very afflictions that threatened to overcome the feebleness of 
man ; how wisely and beautifully balanced, are both moral and 
physical relations ! 

438. The land breeze begins, at evening, to blow towards the 
sea, and continues through the night ; this change is owing to the 
rapid cooling of the air on land, when the sun's rays are with- 
drawn, while the water which had absorbed the heat to a consid- 
depth below its surface, has now a warmer and rarer atmosphere 
than the surrounding coast, and the wind always blows to that 
point where the air is lightest. This subject may be illustrated 
by the following simple experiment. In the middle of a large vessel 
of cold water, put a small vessel filled with hot water ; the former 
representing the ocean, the latter, an island, with the air rare- 
fied by heat. Hold a lighted candle over the cold water (at A) and 
blow it out ; you will see the smoke which represents the denser air, 
moving towards the vessel containing hot water. Now fill the lar- 



437. Land and sea breezes. Sea breeze. Physical and moral relations. 

438. Laud breeze. Experiment illustrating the phenomena of land and 
sea breezes. 

14 



158 



NATURAL PHILOSOPHY. 




Fig. 155. 



ger vessel with warm water, and the 
smaller with cold, and hold the can- 
dle over the hot water (at B,) the 
smoke will move in the direction of 
the warmer atmosphere. 
439. In the torrid zone there is a continual ascent of rarefied 
air, which spreads to the north and south in a direction opposite 
to the trade-winds below. These upper currents becoming cooled 
above, at last descend and mix with the lower air of the northern 
and southern regions, thus restoring to them what they lose by the 
lower currents which they are constantly 
sending towards the equator. In a warm 
room, the same process of cold air com- 
ing in below, and warm air rushing out 
above, is continually going on. 

Hold a lighted candle at the top of an open 
door way, and the blaze will be borne outward 
by the current of rarefied air. Place another 
candle at the bottom of the passage, and tfie 
blaze will be blown inward by the counter cur- 
rent of cold air ; while half way between the 
top and bottom of the passage, the blaze will 
rise perpendicularly, showing that here, there 
is no current of air. 

440. Wind may cause the barometer 
to fall by diminishing atmospheric pres- 
sure, or a quick motion of air in a hori- 
zontal direction may suspend the whole 
or part of its weight ; as a person in skating rapidly, my pass 
over ice that would not bear his weight if he were standing still. 
The force of a current of air is increased, in proportion as the pas- 
sage through which it runs is diminished. 

Take a small tube, (Fi 




Fig. 156. 




156,) open at 
both ends, and blow forcibly through it, 
at the same time let a lighted candle be 
placed near in the tube, and you will 
perceive the flame to be forced towards 
it. While the air within the tube was at 
rest, it exerted a pressure against the 
sides, equal to the pressure of air with- 
out, therefore the two forces balanced 
each other. But when, by blowing 
through the tube, the horizontal motion 
diminished the pressure within, the ex- 
ternal pressure forced the air, and with 
it, the flame of the candle into the ori- 



439. Why does not the air of the polar regions become exhausted, by the 
currents towards the equator ? Experiment showing the currents which are 
in motion in a warm room. 

440. Atmospheric pressure diminished by wind. 



METEOROLOGY. 159 

fice. We perceive therefore, that winds, by diminishing atmospheric pres- 
sure, must effect the barometer. Experience verifies this, for it is found, 
that during high winds the barometer falls rapidly. 



LECTURE XXVII. 

METEOROLOGY. STEAM. ELASTIC FORCE OF STEAM. 

STEAM ENGINE. 

441. Meteorology is that branch of philosophy which treats of 
weather, the formation of vapor, fog, dew, rain and snow ; also of 
thunder and lightning, and other atmospheric phenomena produ- 
ced by electricity. 

442. Evaporation is the slow change of liquids into vapor ; 
boiling is a more rapid process of the same kind. The sun's 
rays falling upon the surface of the land or water, are sufficiently 
powerful to cause evaporation, raising into the atmosphere vast 
quantities of vapor, which serve as a storehouse, from whence 
are sent forth, dew, fog, rain, and snow. Clouds are a collection 
of condensed vapor, which though invisible near the surface of 
the earth, where the heat is greater, and the vapor consequently 
rarer, appears as a dense mass, when cooled in the higher regions 
of the atmosphere. 

443. Fogs are condensed vapor, differing from clouds, only in 
being suspended nearer the surface of the earth. -When the sur- 
face of the earth or water is warmer than the surrounding air, 
the aqueous vapor with which the air, in a greater or less degree, 
is always charged becoming heated by contact with the war- 
mer surface, in attempting to rise, is immediately condensed by the 
colder air around it, and thus &fog is produced. But when the 
air is warmer than the surface of the earth or the water, the va- 
por is not condensed, but rises into higher regions forming clouds. 
The fogs which often prevail at night, arise in consequence of the 
air being cooled more suddenly than the surface of the earth, by 
the absence of the sun. When the beams of the morning sun 
begin to warm the earth, a dense fog sometimes appears ; this 
is because the sun's rays penetrate the air without heating it and 
the earth, in consequence, becomes warmer than the air. We 

441. What is meteoi'ology ? 

442. Evaporation. 

443. Fogs. Fogs at sunrise. Vapor which seems to issue from the mouth 
in breathing. 



160 NATUKAL PHILOSOPHY. 

may now understand, wh} r , in a summer morning, fogs are seen 
hanging over lakes and river ; and, why, in a cold morning, a va- 
por, like smoke, seems to issue from the mouth in breathing : the 
cause in both cases is the same, that is, vapor, meeting with air 
colder than itself, is condensed. 

444. Frost is formed when vapor is condensed as soon as it 
rises and is frozen before it ascends from the surface of the 
earth. 

Dew is produced when the vapor which is formed at the sur- 
face of the warm earth is condensed before it can ascend ; and 
when the surrounding air is not cold enough to congeal it into 
frost. Thus the grass and flowers are often found covered 
with moisture on a summer's morning, though there has been 
neither fog nor rain during the night. A pitcher filled with cold 
water, will be seen, in a warm day, covered with moisture ; the 
outside of the pitcher being colder than the air in contact with it, 
condenses the vapor which the air held suspended. This mois- 
ture is formed upon the same principle as dew ; the cold pitcher 
representing the cold air which condenses vapor arising from the 
earth. 

445. Mist is the vapor of clouds becoming more dense, so that 
the aqueous particles acquire sufficient weight to cause them to 
fall, though they are too small to appear visible, in drops. Rain 
is occasioned by the sudden condensation of aqueous vapor, and 
the consequent union of many minute particles, which, becoming 
more dense are more readily subject to the law of cohesive at- 
traction, and, uniting, form drops ; these drops fall to the earth 
by their own gravity. A wind warmer than the temperature of 
the cloud, will dissolve it into an invisible vapor, while a colder 
wind will condense the vapor, and cause it to fall in drops. 

446. Snow is formed by the freezing of minute particles of vapor 
while they are condensing. Hail is formed by drops of rain, 
which are frozen, in descending, as they pass through regions colder 
than those in which they were formed. In a warm day we are 
sometimes surprised by a hail storm ; this is occasioned by the 
sudden meeting of hot and moist air with a very cold wind. 

447. We find constant changes going on in the atmosphere, by 
the ascent of water in a state of vapor, and its descent, in vari- 
ous forms, upon the earth. Many blessings accompany these 

444. Frost. Dew. Dew upon flowers. Cause of moisture on the out- 
side of a pitcher containing water. 

445. Mist. Rain. Effects of wind in producing rain. 

446. Snow. Hail. 

447. Evaporation a source of novelty and beauty in its effect upon the at- 
mosphere. Condition of the earth should the process of evaporation cease. 
Wisdom of God's providence, and our obligations to gratitude and obedience. 



STEAM. 161 

ckanges ! To them, we owe the variety of coloring which we see 

in tin- clouds, where, blending with the most gorgeous hues, are 
the faintest and most delicate tints which nature presents, or ima- 
gination can paint ; and exhibiting forms, by turns, grotesque, 
picturesque, beautiful and sublime ; — who can tell how much of 
poetical inspiration, of calm delight, and of devout meditation, the 
contemplation of the clouds has afforded to the successive gener- 
ations of men, who, by turns have gazed upon their ctherial forms 
and changing colors. How tame and dull would be the aspect 
of the heavens, were they always to present an unvarying ap- 
pearance, even though this were the beauteous calmness of a 
summer sky ! 

Were the process of evaporation to cease, the earth overcharg- 
ed with moisture, would destroy by this excess the vegetation 
which it now nourishes. There would be no longer rain or dew 
to refresh or purify the air. Mountainous regions, after sending 
forth their watery #)res in rivulets and rivers, would become im- 
poverished and withhold their gifts ; while the ocean, losing noth- 
ing by evaporation, and swollen by supplies no longer taken up, 
would overleap its bounds and extend its dominions over the land. 
Such would be the consequences of an interruption in the wise 
and constant government of God, in this department of nature. 
Yet many of God's creatures, calling themselves rational, never 
reflect, that there is anything in all this to call forth their love, 
or admiration. They are like children enjoying the support 
and protection of a kind and watchful parent, without gratitude, 
or even consciousness of their obligations. There are men who 
can " bear to live, and dare to die," indifferent to the character 
and acquirements of the Being whose providence not only sus- 
tains them by the general and constant laws w r ith which He gov- 
erns " times and seasons," but who watches over the minutest 
circumstances of their existence. 

Steam. 

448. Boiling is a rapid process of converting water into vapor, 
and the vapor thus produced is called steam. We must refer to 
Chemistry for an explanation of the process of boiling, and the 
properties of steam : to Natural Philosophy properly belongs the con- 
sideration of the mechanical agencies of steam. The pressure of 
the atmosphere opposes itself to the formation of steam, and where 
this pressure is removed, liquids can be made to boil with much 
less heat than before. Even the warmth of the hand is found suffi- 
cient to make alcohol boil, when relieved from atmospheric pressure. 

448. Boiling. Atmospheric pressure opposes the formation of steam. 
Pulse-glass. 

14* 



162 



NATURAL PHILOSOPHY. 



Fig. 157. 




The figure represents a pulse 
glass, consisting of a glass tube 
jl with a bulb at each end. Th< 
jfgjl glass is partly filled with alco 
^W* hoi, and the air is expelled b] 
causing the liquid to boil ; the opei 
end is then hermetically* sealec 
There is now a vacuum over the liquid. On holding, in the warn 
hand, the bulb which contains the liquid, it will begin to boil, an< 
steam or vapor will pass over into the cold bulb, where it will b< 
condensed, or again become liquid ; thus the whole contents of on< 
bulb may be transferred into the other. 

449. Liquids boil with less heat in elevated situations than ii 
lower regions, because the pressure of the atmosphere is less 
Under the exhausted receiver of an air-pump, a small increas< 
of temperature will cause a liquid to assume the state of vapor 
450. The peculiar property of steam, and that wjfjch renders it of sucl 
vast importance as a mechanical agent, is its great elastic force. " The nam< 
of steam engine," says Dr. Arnott, " to most persoDS, brings the idea of : 
machine of the most complex nature, and hence intelligible only to thos 
who will devote much time to the study of it ; but he who can understam 
the common pump, may understand a steam engine. It is in fact only ; 
pump in which fluid is made to impel the piston, instead of being impellei 
by it, that is to say, in which the fluid acts as the power, instead of bein; 
the resistance. It may be described simply as a strong barrel, or cylinder, c 
with a closely fitting piston in it, at b ; the piston is driven up and down b; 
steam admitted alternately above and below, from a suitable boiler; whil 
the end of the piston-rod, a at which the whole force may bi 
158. considered as concentrated, is connected in any convenient wa; 
with the work that is to be performed. The power of the en 
s gine is proportioned to the size or area of the piston on whicl 

the steam acts, with a force according to the density, of from 1, 
to 100 or more pounds to each square inch. 

In some of the Cornish mines, there are cylinders and piston 
of more than ninety inches in diameter, on which the pressun 
of the steam equals the efforts of six hundred horses. " Some 
times the wonderful piston-rod may be seen acting upon one en< 
of a great vibrating beam, with the other end of which, immensi 
water-pumps are connected, whose motion causes almost a rive 
to gush up from the bowels of the earth. At other times work 
ing a crank, it is seen urging complicated machinery ; and om 
engine, stretching long arms over a great barrack or manufac 
tory, will keep thousands of spinning-wheels in motion, while a 
the same time it is carding the material of the thread, and weav- 
ing the cloth. In like manner one steam engine in a grea 

* That is, seale i by melting the glass at one end, and closing it when in i 
soft state. 

449. Why will liquids boil with less heat in elevated situations than ii 
lower regions and with a small increase of temperature under the air-pumj 
receiver. 

450. Elastic force of steam. Steam engine compared to a pump. Hov 



Fig. 




STEAM ENGINE. 163 

metropolitan brewery, may be seen at once grinding the malt, pulling 
up supplies of all kinds from wagons around, pumping cold water into some 
of the coppers, sending the boiling wort from others up to lofty cooling pans, 
perhaps also working the mash-tub, drawing water from the deep wells un- 
der ground, loading the drays, and in a word, performing the offices of a 
hundred hands. 

" Again there are manufactories where this resistless power is 6een, with 
its mechanic claws seizing masses of iron, and in a few minutes delivering 
hem out again, pressed into thin sheets, or cut into bars or ribands, as if the 
iron had become to it like soft clay in the hands of the potter. One steam 
engine, four miles from London, is at the same instant filling all the water 
reservoirs and baths and fountains of the finest quarter of the town. And 
for some years now, in all parts of the world, has this wonderful piston-rod, 
working at its cranks, been turning the paddle wheels of innumerable steam- 
boats, thus setting at defiance the violence of the winds and waves, and the 
currents of the fleetest rivers, while it carries men and civilization into the 
remote recesses of all the great continents. Wherever a river leads, the re- 
gion watered by it, although concealed, perhaps, since the beginning of the 
world, are now called by the steam engine from their solitudes, to form parts 
of the great garden, which civilized man is beautifying. Such are a few 
of the prodigies which this machine is already performing, and every day is 
witnessing new applications of its utility. 

451. " It regulates with perfect accuracy and uniformity, the number of its 
strokes in a given time, counting or recording them moreover, to tell how 
much work it has done, as a clock records the beats of its pendulum, it regu- 
lates the quantity of steam admitted to work ; the briskness of the fire ; the 
supply of water to the boiler; the supply of coals to the fire ; it opens and 
shuts its valves with absolute precision as to time and manner; it oils its 
joints; it takes out any air which may accidentally enter into parts which 
should be vacuous; and when anything goes wrong which it cannot of itself 
rectify, it warns its attendants by ringing a bell ; yet with all these talents 
and qualities, and even when exerting the power of six hundred horses, it is 
obedient to the hand of a child ; its aliment is coal, wood, charcoal or other 
combustibles ; it consumes none while idle ; it never tires, and wants no 
sleep ; it is not subject to malady when originally well made, and only re- 
fuses to work when worn out with age ; it is equally active in all climate?, 
and will do work of any kind ; it is a water-pumper, a miner, a sailor, a cot- 
ton spinner, a weaver, a blacksmith, a miller, &c. &c. ; and a small engine 
in the character of a steam poney, may be seen dragging after it on a rail 
road, a hundred tons of merchandise, or a regiment of soldiers, with greater 
6peed than that of our fleetest coaches. It is the king of machines, and a 
permanent realization of the Genii of eastern fable, whose supernatural 
powers were occasionally at the command of man." 

452. " The chief parts of the engine are the boiler A, the cyl- 
inder C, the piston-rod I J, the condenser L, and the air-pump M. 
B, is the steam-pipe, branching into two arms, communicating 
respectively with the top and bottom of the cylinder, and K, is 

does the figure illustrate the action of a steam engine ? To what is the power 
of the steam engine proportioned ? Various operations of steam engines. 
Application of steam power applied to manufactories. Steam power applied 
to navigation. 

451. The steam engine regulates and records its own motion, &c. 

452. Describe the parts of the steam engine. 



164 



NATURAL PHILOSOPHY 


Fig. 159. 


T f 




J 






the eduction-pipe,* formed of the two branches which proceed 
from the top and bottom of the cylinder, and communicates be- 
tween the cylinder and the condenser. N, is a cistern or well of 
cold water in which the condenser is immersed. Each branch 
of pipe has its own valve, as F, G, P, Q, which may be opened 
or closed as the occasion requires. 

453. " Suppose, first, that all the valves are open, while steam 
is issuing freely from the boiler. It is easy to see that the steam 
would circulate freely throughout all parts of the machine, expell- 
ing the air, which would escape through the valve in the piston 
of the air-pump, and thus the interior spaces would all be filled 
with steam. This process is called blowing through; it is heard 
when a steamboat is about setting off. Next the valves, F, and 
Q. are closed, G and P, remaining open. The steam now pres- 
sing the cylinder forces it down, and the instant when it be- 
gins to descend, the stop-cock O, is opened, admitting cold water, 
which meets the steam as it rushes from the cylinder and effect- 
ually condenses it, leaving no force below the piston, to oppose 
its descent. Lastly, G and P being closed, F and Q are opened, 
the steam flows in below the piston, and rushes from above it 
into the condenser, by which means the piston is forced up again 
with the same power as that with which it descended. Mean- 
while the air-pump is playing, and removing the water and 
air from the condenser, and pouring the water into.a reservoir, 
whence it is conveyed to the boiler, to renew the same circuit."f 

* From educo, to draw out. 
t Olmsted. 



453. Operation of the steam engi 



SUCTION PUMP. 



165 



LECTURE XXVIII. 



Fig. 



160 



ATMOSPHERIC PRESSURE UPON WATER. PUMPS. SYPHONS. 

Pumps, 

454. We have seen, in examining the barometer, that the pres- 
sure of the atmosphere is sufficient to support a column of 30 inches 
of mercury, and a column of about 34 feet* of water. It is upon this 
principle that we account for the rise of water in a pump, when 
the air within is removed by the operation of pumping, and the 
weight of external air meeting with no counteracting force presses 
the liquid upward into the vacuum. 

455. It is a familiar fact that liquid may be drawn from a cask 
or any other vessel by means of a straw, or other tube applied to 
the surface of the liquid, and at the same time held to the mouth. 

The air being first withdrawn from the tube by suction, the 
liquid rushes up to fill the vacuum. 

Suction Pump. 

The common household pump consists of a large 
tube, E, in which is a piston made to fit, air-tight, 
the bore of the tube. In the piston is a valve, C, 
opening upwards like a trap-door, which allows the 
air and water to rise through it, but not to descend. 
This piston, sometimes called the bucket, is moved 
up and down by a rod fastened to a handle or lever. 
The pump usually consists of two parts ; the upper 
and wider part, E D, is called the pump-barrel ; 
the piston moves in this ; the part of the pump, D B, 
which is smaller in diameter, is called the suction- 
tube. At the joining of these two parts, is a fixed 
valve, D, which opens upwards. E, is a pipe or 
spout, serving as a passage for the water which is 
raised. 

456. The parts of the pump being now described, 
we will consider its mode of operation. When the 
piston is let down as low as the fixed valve, D, both 
valves are closed by their own weight. Let the pis- 
ton now be drawn up as at C, and the column of air 

* Some writers say 32 feet, some 33 feet; — 34 feet is undoubtedly the 
maximum height to which a column of water can be raised by atmospheric 
pressure. 

454. To what height will the pressure of the atmosphere support mer- 
cury or water ? On what principle does water rise in a pump ? 

455. Suction. Describe the suction-pump. 
458. Its mode of operation. 




n/\rO 



166 



NATURAL PHILOSOPHY. 



which rested upon it is also raised, leaving a vacuum between C 
and D ; the air below D being relieved from pressure, expands, 
and lifting up the valve, D, passes through it and fills the vacuum. 
A few strokes of the piston thus exhausts the pump of air, and the 
water, relieved from its weight, is forced upward by the pressure 
of the incumbent atmosphere. Rushing up through the suction- 
tube, the water lifts the valve, D, and enters the pump-barrel. 
When the piston now descends, it presses upon the water, which 
not being able to return through the valve D, pushes up the valve 
C, and when the piston is next raised, all the water above it is 
lifted up, and begins to escape through the spout E ; thus when 
the piston is raised, the valve D rises and the valve C falls ; 
and when the piston is depressed, D falls and C rises. 

457. It should be observed, that although the water is raised 
into the pump-barrel by the pressure of the atmosphere, it is lifted 
from thence to the level of the spout by means of strength exerted 
upon the piston. Therefore, as the pressure of the atmosphere 
will sustain a column of water about thirty-four feet in height, the 
valve at the top of the suction-tube may be this distance from the 
surface of the water in the well ; and as the water after passing 
above the suction-tube, is raised by lifting, the height to which it 
is afterwards carried will depend on the length of the piston-rod 
and the degree of strength employed. When we say that water 
will not rise in a pump above thirty-four feet, we mean only that 
atmospheric pressure will not raise it above that distance. 

The Forcing-pump. 

458. The forcing-pump consists of a bar- 
rel, A B, and a piston or forcer, C. There 
are two fixed valves, one at D, and the other 
at S, in the branching-pipe V. The piston 
is solid, or without any valve, therefore the 
water cannot rise above it. When the pis- 
ton is pressed down, the air between that and 
the valve, being subjected to pressure, opens 
the valve, S, and passes out at the branching- 
pipe. Thus the valve S, answers the same 
purpose as the piston-valve of the suction- 
pump, and the process of raising the water 
until it ascends through the valve D, is the 
same as that which takes place in raising it 
into the barrel of the suction-pump. But the 
water being pressed upon by the piston in the 

457. Can water be raised in a pump higher than thirty-four feet ? 

458. Describe the forcing-pump. How is the water in a forcing-pump 
made to flow out in a 6teady current ? 




-vijion. 167 

barrel of the forcing-pump, and having no other vent, is forced 
through the valve S. As the operation of a pump consists 
in applying power by separate efforts, it is evident that the 
water will not flow out in a steady current. The irregular 
discharge is remedied by the addition of an air-vessel, U, into 
which is fitted a small pipe, T, reaching nearly to the bottom of 
the vessel. This vessel, by the action of the pump, will at first 
be filled with condensed air ; when water is forced in through the 
valve, S, it confines the air in the upper part of the vessel ; on the 
admission of more water, the condensed air presses by its elasti- 
city on the surface of the water which cannot return through the 
valve S, and is forced up the pipe T, in a steady stream. Thus, 
the condensed air first receives the force given by the piston, and 
reacts by its elasticity, like a spring upon the surface of the water, 
with a nearly uniform power. 

459. The fire engine consists of two forcing-pumps, working 
together, which throw/ the water into an air vessel, from whence 
it passes into two, long, leathern tubes, called the hose. The hose 
may be pointed in any direction, and water thrown by the forcing 
pumps, to the roofs of the highest buildings. 

460. There is a very simple instrument called 
Fig. 162. a syphon, the action of which depends on the 
pressure of the atmosphere. It is used for draw- 
ing off liquors from one cask into another. Sup- 
pose a b, to be a tube having two arms of une- 
qual length ; this tube being filled with water, 
and the mouth of the shorter arm immersed in 
a vessel filled with any liquid, the liquid w 7 ill 
run out until the vessel containing it is emptied. 
The cause of this action of the syphon may be 
I K — W thus explained. The liquid, which, at first, filled 
the longer arm, w r ould flow out by its own gravity, 
and a vacuum being left, the pressure of the atmosphere upon 
the surface of the liquid within the vessel, would force that in 
the shorter arm of the syphon over the top ; the same cause 
would continue to sustain the shorter column, and to impel the 
liquid over the top until the whole was exhausted. 

461. This effect may be produced w r ith any similar, bent tube, 
provided the shorter arm or column be less than thirty-four feet 
in length, otherwise the force of atmospheric pressure would be 



459. Fire engine. 

460. Describe the syphon. 

461. Why must the short arm of the syphon be less than thirty-four feet ? 
Why must a syphon for drawing mercury be shorter than for drawing water ? 
Syphon with a suction-pipe. 




168 



NATURAL PHILOSOPHY. 




Fig. 164. 



insufficient to force the liquid through the tube 
Mercury may be drawn through a syphon ii 
the same manner as water, but as this fluid i; 
nearly 14 times heavier, the height of the sy 
phon in this case must be proportionally short 
ened, since the mercury w T ouid only rise abou 
thirty inches, as in the barometer. Syphon 
are sometimes made with a suction-pipe as at a 
in which case a vacuum may be formed in th< 
shorter arm, by the mouth. 

462. An amusing toy called Tan 
talus 7 cup,* represents the figure of i 
man standing in a cup. The handle o 
the cup is a syphon, the short arm o: 
which is nearly level with the mouth o: 
the figure ; the liquid can never read 
the mouth of the figure as it flows ou 
thiough the syphon handle. 

463. Intermitting springs or foun 
tains, are caused by drains in the eartl 
communicating with reservoirs of water 
These drains may be considered as na 
turai syphons, which acted upon by at 
mospheric pressure, carry off the water 
and then cease flowing, until rains o 
the melting of snows have again fille< 
the reservoirs. 



Synopsis. 

464. 1. Pneumatics treats of the mechanical properties oj 
elastic fluids, chiefly of air. 

2. Air is matter, because it is extended and impenetrable. 

3. Air is invisible, because it is thin and transparent. 

4. Air possesses weight ; it is compressible and elastic. 

5. The elasticity of air, increases with its density. 

6. The density of the air diminishes upwards ; or its pressure 
is in proportion to its depth. 

* Tantalus, in mythology is represented as having, for an offence agains 
Jupiter, been plunged from a state of happiness into one of torment. Hi 
greatest punishment was that of everlasting thirst; being condemned to se 
a pure stream forever rising to his lips, but flowing back as soon as he a 
tempted to drink of it. 

462. Tantalus' cup. 

463. Intermitting springs. 
484. Synopsis of Pneumatics. 




SYNOPSIS. 169 

7. The air like water presses in all directions. 

8. The pressure of the atmosphere on fluids causes the rise of 
WtUer in pumps, and of mercury in the barometer. 

9. The air-pump is an instrument used for exhausting the air 
from any vessel, 

10. A vacuum is an empty space, or generally understood to 
mean a space emptied of air. 

11. ^1 condenser is an instrument used for the purpose of press- 
ing more air into a vessel; the air is said to be condensed, 
when heavier than common air. The operation of the air- 
pump and condenser are directly opposite, because the former 
rare lies, and (he latter condenses air. 

12. The barometer measures the weight of the atmosphere, the 
thermometer its temperature. 

15 



PART V 

ACOUSTICS. 



LECTURE XXIX. 

SONOROUS BODIES. BELLS. MUSICAL STRINGS. JEOLIAN HARP. 

465. Acoustics is a word derived from the Greek, and signi- 
fies the science which treats of sounds. 

This subject opens to us a train of moral reflections, as well 
as a curious and interesting field of scientific inquiry. The ten- 
der accents of affection, the solemn tones of prayer, the thrilling 
notes of music, the pealing of bells, and the burst of thunder 
all, are but vibrations of air. Deprived of sound, what a gloomy 
vacancy would exist in creation, and be felt in the heart of man ! 
How grateful to our hearts is the music of nature, as heard in the 
lively carol of birds, the lowing of kine, with all the variety ot 
sounds by which the brute creation, in their own true and ex 
pressive language, manifest their emotions. Inanimate nature 
too, seems by this wonderful gift of sound, to be endued with 
life and intelligence; the brook softly murmurs in its placid 
course, — the cataract in startling thunderings proclaims its tre- 
mendous force ; — the light foliage responds to the gentle music 
of the summer's breeze ; and bending forests, in mournful and 
mysterious tones, waft to our spirits, upon the wings of the au- 
tumnal blast, thoughts of the majesty and power of Him, " who 
walketh on the wings of the wind." 

466. But interesting as is the voice of animate and inanimate 
nature, we value sound, chiefly, for the power it gives mind of 
communicating with mind. As sensation is to the soul the medium 
of holding communion with external objects, so is sound among 
human beings, and among the lower orders of animals, the link 

465. Definition of acoustics. Moral reflections upon sound. 
4fifi Chief value of sound. 



SONOROUS BODIES. 171 

which connects their sympathies, the chain which binds their 
affections. To this power, we are indebted, not only for spoken 
language, but tor its subsequent expression in written characters, 
ami, consequently, for all human sciences. 

" The air is vehicle of sound : 
Remove but the elastic pulse of air 
And the same ear which now, delighted, feels 
The nice distinction of the finest notes, 
Would not discern the thunder from a breeze." 

467. 1. Bodies which produce sound are called sonorous 
bodies. 

2. Air is the common medium which transmits sound ; 

3. The ear is the organ which receives the impression of sound. 

4. The mind, only, is capable of the sensation produced by 
sound ; — 

5. This sensation is called hearing. 

Sonorous Bodies. 

468. Those bodies are properly called sonorous which afford a 
sound distinct, and of some duration ; such as bells, and the 
strings of musical instruments. Bodies which cause only a con- 
fused noise, like that of a stone falling upon a pavement, are not 
called sonorous. Thus philosophers make a distiction between 
sound and noise. 

469. Sound is supposed to be produced by motion in the air 
caused by vibrations of the sounding body. Gold, brass, copper, 
silver, iron, and glass, being dense and elastic, are sonorous ; 
while lead and wax being softer, are less capable of vibratory 
motion, and give only a confused and imperfect sound. 

470. The vibration of a sonorous body gives a tremendous mo- 
tion to the surrounding air, similar to that caused by throwing a 
stone into smooth water ; the undulations becoming weaker the 
farther they are from the centre of the motion. It is proved that 
the intensity of sound decreases in the inverse ratio of the square 
of the distance ; as, at 2 rods distant, the sound is 4 times weaker 
than at one rod distant, and at 3 rods distant, it is 9 times 
weaker. 

471. The waves of air producing sound, differ, in this respect, 
from the undulations of water, viz ; air being elastic, its motion 
does not consist of regularly extending waves, but of vibrations, or 

467. Repeat the five propositions respecting sound. 

468. Sonorous bodies. Difference between sound and noise. 

469. Cause of sound. 

670. Intensity of sound decreases in the ratio of the distances. 



172 



NATUJRAL PHILOSOPHY. 



Fig. 165. 




motions backwards and forwards, like those of the sonorous 
body which produced them. 

Figure 165 represents waves of sound ; di- 
verging from the point A they become weaker, 
as rays of light become fainter as they are 
more diffused. The points a, b, c, &c, with 
the intermediate spaces, represent undulations 
of air spreading in concentric circles. Each 
particle of air on receiving an impulse either 
directly from the sonorous body or by trans- 
mission, becomes agitated, moves back and forth like an oscilla- 
ting pendulum, within a limited space, and at length ceases to 
move. But this particle has communicated motion to contiguous 
particles, which, in their turn, vibrate and communicate motion. 
On account of the extreme rarity and elasticity of air, vibrations 
of sound extend to a much greater distance than the circular 
waves of water. The undulations of air are also in a sphere 
extending upwards and downwards, as well as outwards, while 
those of water extend only upon a horizontal plane. 

Bells. 
472. It may at first thought, appear incredible that a bell ac- 
tually changes its form every time it is struck ; but this circum- 
stance causes its sound. If light particles of dust lie upon the 
outside of a bell when it is struck, they may be seen to be agita- 
ted, which shows that the particles of the bell are in motion. A 
small bit of cork suspended to a bell, will be tossed back and forth 
when the bell is sounding, like a pendulum in motion. 

473. Suppose the bell to be struck on 
the outside, at the point a ; this part will 
tend towards g, while the parts b and d, 
tend towards i and m, and this action on 
these parts carries the point c, towards e. 
Though these parts soon spring back, on 
account of the elasticity of the metal, they 
have acquired a momentum which keeps 
them in motion ; as the part a, having 
returned from g to a, tends towards f ; 
the part c towards h ; and the parts b and 
d, towards Jc and I. Thus, though the 
base of the bell is a circle, by being struck 

471. Waves of air differ from those of water. What does Fig. 165 re- 
present ? How is sound transmitted through the air ? 

472. What proves that the particles of a bell when it is sounding are in 
motion ? 

473. Describe Fie:. 166. 




MUSICAL STRINGS, 173 

it is changed into an ellipse (or oval form) of which the diam- 
ater is alternately longer in different directions. These ellipses 
grow smaller and smaller, like the vibrations of a pendulum when 
no longer acted upon by any moving power, until the particles 
reusing to vibrate, the sound dies away. When a large bell 
rings, we perceive a mingling of sounds ; this is owing to the 
difference in diameter of the upper and lower parts of the bell. 
We may consider a bell as composed of a series of rings placed 
one above another; those nearer the base having the greater 
circumference, perform their vibrations more slowly than the up- 
per and smaller rings, consequently causing a variation in the suc- 
cession of sounds. 

Musical Strings. 

474. The vibrations of musical strings are often visible to the 
eye, and when this is not the case, their existence may be prov- 
ed by experiment ; as fine sand, or bits of paper, will be thrown 
from the strings of a sounding violin or harp. 

The elasticity of any string 
Fig. 167. causes a series of vibrations, 

and therefore continuance of 
sound. Suppose a b, to be 
an elastic string fastened at 
the two ends ; on drawing this 
string toward c, and then let- 
ting it go, it springs back to 
its straight position ; but hav- 
ing acquired a momentum like 
that of a vibrating pendulum, instead of resting here, it passes 
towards d, nearly as far in the opposite direction. This is one 
vibration ; the momentum then acquired produces other vibra- 
tions, each less than the former, until the resistance of the air 
and the friction of the string overcome the velocity, and the 
string rests in the original position, a b. 

475. Sound is produced by vibrations in this manner ; the 
string strikes against the particles of air which are contiguous 
to it, these particles being condensed by the pressure, and im- 
pelled forward, agitate the surrounding atmosphere ; each agi- 
tation affects the contiguous parts, until the whole mass, within a 
certain distance, assumes a tremendous motion. Thus sound 
does not proceed from a progressive motion of air, but from a se- 
ries of contractions and expansions of air. 




474. Vibrations of musical strings. Causes of vibrations in strings. 

475. How is sound produced by vibrations ? 

15* * 



171 



NATURAL PHILOSOPHY. 



476. When any sonorous body 
points or lines in its surface which 

Fig. 108. 




vibrates, there are certain 
remain at rest. These may 
be exhibited by experiment ; 
let a pane of window glass 
be thinly covered with very 
fine sand, and the bow of a 
violin drawn across its edge ; 
the moment a clear sound 
is produced, a part of the 
sand will be thrown off the 
glass by its vibration, while, 
in certain places, it remains 
undisturbed, forming a regu- 
lar figure. The higher the tone, the more complicated the fig- 
ure ; thus the figure at A is less complex than at B. Another 
very simple experiment proves also that in vibrating bodies 
there are certain natural stops or rests ; let a tumbler be partly 
filled with water, and draw the wet finger across its edge until a 
sound is produced. The vibrations of the water will be seen to 
proceed from certain regular points, while there are other points 
in which the water remains undisturbed. 

477. A long, vibrating, musical string, thus divides itself into 
parts, with points of rest between them, on which points, bits of 
paper will remain, though they will be thrown by the vibrating 



Fig. 169. 




motion from every other part. Thus suppose a b, to be such a 
string, the part from a to d, vibrates as though it were fixed at 
d, and so on from d to c, and c to b. The sounds thus belong- 
ing to a single cord or string, and produced by its spontaneous 
division into different parts, constitute when heard together, or 
in succession, the simple music of nature itself. It is produced 
in the most perfect manner by the instrument called the JEolian 
harp. 

" This is a long box or case of light wood, with harp or violin strings ex- 
tended on its face. These are generally tuned in perfect unison with each 
other, or to the same pitch, excepting one serving as a bass, which is thicker 
than the others, and vibrates only half as fast ; but when the harp is sus- 



476. Regular figures produced by a vibrating body. 

477. Natural rests in vibrating strings. jEolian harp. 



MEDIUM OF SOUND. 175 

pended among trees, or in any situation where the fluctuating breeze may 
reach it, each string according to the manner it receives the blast, sounds 
either entire, or breaks into some of the simple divisions thus described ; 
the result of which is the production of the most pleasing combination and 
succession of sounds that ear has ever listened to, or fancy perhaps, con- 
ceived. After a pause, this fairy harp may be heard beginning with a low 
and solemn note, like the bass of distant music in the sky ; the sound then 
swelling as if approaching, and other tones breaking forth, mingling with 
the first, and with each other, in the combined and varying strain. Some- 
times one clear note predominates and sometimes another, as if single musi- 
cians alternately led the band : and the concert often seems to approach, 
and again to recede, until with the unequal breeze it dies away and all is 
hushed again. It is no wonder that the ancients who understood not the 
nature ot air, nor consequently of simple sound, should have deemed the 
music of the iEolian harp supernatural, and in their warm imaginations, 
should have supposed that it was the strain of invisible beings from above, 
descended in the stillness of evening or night to commune with men in a 
heavenly language of soul, intelligible to both."* 



LECTURE XXX. 

MEDIUM OF SOUND. THE EAR. ECHO. SPEAKING TRUMPET. 

VELOCITY OF SOUND. MUSIC. THE HUMAN VOICE. 

Medium of Sound. 

478. Air is the common medium by which sound is transmitted ; 
or, in other words, the vibrations of sonorous bodies cause similar 
vibrations in the air, which, striking upon our organ of hearing 
produce a sensation in the mind. Sensation is the parent of per- 
ception ; thus the sensation caused by vibrations of air produces 
a perception of sound ; emotions follow these sensations and per- 
ceptions, varying according to the nature of the sounds which are 
thus mysteriously linked to the mind. 

479. When we hear the sound of a musical string, the ear re- 
ceives from the air, as many strokes as the string performs vibra- 
tions in the same time. If the string perform 100 vibrations in a 
second, the ear will receive the same number of impressions 
within the same period. 

480. The sound of a bell struck under the receiver of an air- 
pump becomes weaker as the air is exhausted, until the sound 

* Arnott. 

478. Medium of sound. Process of the mind in obtaining a perception 
of sound. What follow perceptions ? 

479. How do vibrations affect the ear? 

480. Bell under an exhausted receiver. Sound more powerful as air is 
more dense. 



176 NATURAL PHILOSOPHY. 

ceases entirely. On admitting air into the receiver, the bell will 
again be heard. When air is more dense than common, as in the 
receiver of a condenser, and in the diving-bell, sound is more 
powerful. In accordance with this law, it is observed, that on 
high mountains, where the air is light, sound is feeble. The 
travelers among the Alps say, that when near enough to see a 
huntsman on the neighboring cliff and observe the flash of his 
gun, the report is sometimes so faint as scarcely to be audible. 
In caverns and mines, where the air is usually dense, slight 
sounds appear louder and clearer than at the surface of the earth. 

481. Liquids convey sounds with greater velocity than air. 
The sound of a bell rung under water, and the strokes of work- 
men in a diving-bell, are heard by the people above. Fishes hear 
the slightest sounds, as the angler may observe, when, upon the 
least agitation of the water above them, they are seen to dart off 
in quest of a more quiet retreat. 

482. Solids convey sounds with greater velocity than air or 
liquids. A long train of iron tubes was laid for the purpose of 
conveying water to Paris. Biot,* a philosopher of great research, 
took advantage of this circumstance, to ascertain the exact differ- 
ence between the power of air, and of metal, to transmit sounds. 
He hung a small bell at the end of the iron tube, in such a situa- 
tion, that the clapper struck against the tube, and the side of the 
bell at the same instant. The sound of the bell was conveyed 
through the column of air inclosed within the tube, while the 
iron, itself, transmitted the sound made by striking the tube. By 
the person stationed at the other end of the tube in order to ob- 
serve the succession of the two sounds, it was ascertained, 
that iron transmits sound with about ten times the velocity 
of air. 

If a person at one end of a log, scratch the wood lightly with 
a pin, the sound will be heard distinctly by another person whose 
ear is applied at the other extremity, though the air, itself, would 
not transmit so feeble a sound. By applying the ear to the 
ground, the tread of men and horses may be discovered, which, 
otherwise, could not be perceived. Savages avail themselves of 
this fact, to ascertain the approach of enemies, and animals in- 
stinctively resort to this method for discovering their prey. Pre- 
vious to the great eruption of mount Vesuvius which buried Her- 
culaneum and Pompeii, the animals in that region appeared much 

* Pronounced Be-o. 

481. Sounds conveyed by liquids. 

482. Sounds conveyed by solids. Biot's experiment. Examples of the 
power of solids to convey sounds. Musical boxes. Sounding boards. Ex- 
periment with an iron poker. 



Tin: n \u. 177 

disturbed, owing to the agitation of the earth, produced by dis- 
tant, subterraneous explosions, and conveyed, by the ground, to the 
rais of these accurate observers. 

Musical boxes give much louder tones when placed upon a 
table or other solid body, than when air, alone, is the conducting 
medium of sound. The vibrations communicated from the box, 
spreading throughout the particles of wood, cause a more extend- 
ed surface to act upon the air. For this reason, musical in- 
struments, as violins, guitars, &c, are furnished with sounding 
boards. If one end of an iron poker be placed on the lid of a 
kettle, and the other end held to the car, the boiling of water 
within the kettle, will produce a sound louder than the rattling of a 
carriage over a pavement. 

483. The power of solid bodies to conduct sounds, has led to 
the invention of an instrument called the stethoscope,* or chest- 
inspector, the object of which is, to convey, accurately, to the ear, 
the sounds produced by the motion of the heart, and the blood- 
vessels, situated near the organ. It consists of a simple wooden 
cylinder, one end of which, when used, is applied to the breast, 
while the ear of the physician rests upon the other end. " The 
action going on in the chest," says Dr. Arnott, " are the entrance 
and exit of the air in respiration, the voice, the motion of the 
blood in the heart and blood-vessels ; and so perfectly do these 
declare themselves to a person listening through the stethoscope, 
that an ear once familiar with the natural and healthy sounds, 
instantly detects certain deviations from them. Hence this instru- 
ment becomes a means of ascertaining certain diseases in the 
chest, almost as effectually as if there were convenient windows 
for visual inspection." 

484. " He who planted the ear," or the organ of hearing, is 
also the Creater of the air, or common medium of sound, and 
with that nice adaptation of means to ends which we behold in 
ail the works of this mighty Architect, we find this organ 
wonderfully fitted to collect and concentrate the waves of air 
caused by vibrations of sonorous bodies. The human ear is a 
curious machine, far exceeding in its external construction the 
most delicate work of human art ; and in addition to its vari- 
ous parts, all tending to promote the object of hearing, there is 
an invisible link connecting it with the mind, of the nature of 
which we can have no conception. And, yet, there have been 
men, and those calling themselves philosophers, who, contrary 

* From the Greek steihos, the breast, and sTcopio, to examine. 

483. Stethoscope. 

484. The ear a machine evincing design. 



178 



NATURAL PHILOSOPHY. 



Fig. 170. 




to the dictates of common sense and the word of divine revela- 
tion, have asserted that there is, in the universe, no great designer, 
but, that its creations are the product of mere chance or accident. 
From such philosophers, and from such philosophy, may the youth 
of America be defended ! 

485. We will now examine the parts of the ear, as they are 
manifest by external observation, and anatomical dissection. 

1st. We perceive, on looking into 
the ear,- a wide mouthed tube, a. 
This is an ear-trumpet, the wide 
mouth of which serves to collect 
the waves of sound concentrated at 
the bottom or nervous part of the 
ear-tube. This tube, by the action 
of certain muscles, is moveable by 
many animals, so that it can be direct- 
ed towards the point whence a sound 
proceeds. 
2d. The tympanum or drum of the ear, b, is a tight drawn 
membrane situated at the bottom of the ear-tube, upon which 
the concentrated sound falls, and causes its vibration. The air 
within the drum communicates with the external air, by an open 
passage f, called the eustachian tube, which leads to the back of 
the mouth. When this tube is obstructed by wax, a degree of 
deafness is produced, and the cracking noise and return of acute 
hearing which is often caused by sneezing or coughing, is the 
effect of the removal of this obstruction. 

3d. At e is the vestibule or entrance into the labyrinth ; this 
is connected with the drum of the ear by a chain of four small 
bones, which serves to convey to the labyrinth, the vibrations from 
the drum. 

4th. The labyrinth is that complex, inner compartment of the 
ear, over which, the nerve of hearing, or auditory nerve, is spread, 
as a lining. This nerve, like the optic nerve of the eye, is a con- 
necting link between the organ of sense, and the great sensorium, 
the brain. The labyrinth is filled with water, so that when the 
membrane of the drum, acting upon the chain of small bones, 
compresses the portion of water ,next the chain, the pressure is 
instantly felt throughout the whole mass of water, and, thus, the vi- 
bration is conveyed to the lining of the labrynth, or the organ of 
hearing. The labyrinth consists of the vestibule, e, the three 
semicircular canals, c, which are imbedded in the hard bone, and 
the cochlea, d, which is a winding cavity, like a snail shell. In 



485. Parts of the ear. 
Tbe labyrinth ; its parts. 



Tube of the ear. Drum of the ear. Vestibule. 



REFLECTION OP SOUND. 17<J 

this cavity arc fibers stretched across, like harp strings, these are 
called the lyra. 

486. We judge of the distance of sound by its intensity. The 
capable of determining the direction from which sound 

ds. When we are doubtful respecting a sound, we turn 
the mouth of the ear-tube towards the point from which it 
seems to issue, and thus learn its nature, distance, direction and 
intensity. 

The phenomena of hearing, considered as a "sensation of the 
mind, belongs to the science of mental, rather than mathematical 
philosophy. 

Reflection of Sound. 

487. An echo is a reflected sound. Waves of sound or undu- 
lations of air moving forward, meet with some solid body and are 
thrown back, as waves of water are repelled by the river bank, 
or, as a marble rebounds, when thrown upon pavement. 

According to a law of motion, when an elastic body strikes 
perpendicularly, against a hard substance, it is reflected back in 
the same direction ; but when it strikes obliquely, it is thrown off, 
obliquely, in the opposite direction ; the angle of reflection being 
equal to the angle of incidence. The same law may be applied 
to sound. Suppose a bell, <z, to be struck, 
and the waves of air to fall perpendicularly 
upon .a wall, c ; they would be reflected 
back, in the line c a. A person situated 
at any point on this line, would first hear 
the sound of the bell by means of the 
waves of air caused by its vibration, and, 
again, would hear the same when reflected 
from the wall. But suppose the bell to 
be at &, the waves of sound would strike 
obliquely upon the wall, as in the line c b, 
and the reflected sound would go off, in an 
oblique direction, upon the other side. Sounds uttered by one stand- 
ing in front of a building, will be returned in a right line, and the 
echo will be heard, at a certain distance, by the person speak- 
ing ; but let the person stand, in such a position, that the vibration 
of sound will fall upon the wall obliquely, lie will not hear the 
echo, though another, standing as far on the opposite side, would 

486. How do you judge of the distance of sound? 

487. What is an echo, and how caused ? Manner in which sound is re- 
flected. In what case an echo will be heard by a person who utters the 
sound which is reflected ? What i? nece?snvy in order to produce a perfect 
echo ? Speaking in a crowded room. 




180 



NATURAL PHILOSOPHY. 



Fig. 172. 



hear it ; — thus, one person at the side of a mirror, sees tne image 
of another standing on the opposite side, though he does not see 
his own image. 

As a wave of sound rebounds according to the same law as a 
wave of water or an elastic ball, in order that an echo may bo 
perfect, the surface producing it must be smooth, and of some 
regular form. The various articles of furniture in a room, espe- 
cially those of a soft texture, as carpets and curtains act unfavor- 
ably upon the vibrations which produce sounds. The labor of 
speaking audibly in a crowded room, is greater than in an empty 
one, the power of sound being much heightened by the vibrations 
of bare walls. 

488. Plane and smooth surfaces reflect sound without either 
dispersing or collecting it ; convex surfaces disperse, and concave 
surfaces collect sound. Plane, convex, and concave mirrors reflect 
light in a similar manner ; for which reason, we see a true image 
in a plane mirror, a magnified and distorted one in a concave mir- 
ror, and a miniature image in a convex mirror. 

Suppose e g, to be a smooth, 
concave surface, and that waves 
of sound fall upon a, b, c, d ; these 
will be collected and brought to a 
focus* at fi and here the echo, or 
reflected sound is most perfect. 
Sound proceeding from the center 
of a circle is reflected to this point, 
hence in a large, circular room, we 
may expect in the center, a power- 
ful echo. The room should be 
large for this effect to be produced, because sound moves with 
such velocity that, in a small space, the reflected sound follows the 
direct sound so rapidly, that they blend together, and form but 
one. We shall notice this fact further, in treating of the velocity 
of sound. 

489. An oval, or ellipse, has two centers, or foci,-f one towards 
each end, as a and b, (Fig. 173); and the nature of a curve is such 
that sound, light, or heat, proceeding from either of the foci, as a, is 
all directed, after reflection, at the various points, c, d, e, to the other 
focus, b. A whisper uttered in one focus of an oval room, may, 

* A central point. 

t The plural of focus. 




488. Reflection from plane, convex, and concave surfaces, 
effect of sound falling upon a smooth concave surface. 



Describe the 



489. Round reflected from an oval. 
Fable of Echo. 



W hispering gallery. Ancient oracles. 




IFSAKIXa TiiL'311'KT, AM) EAB TRUMPET. 181 

therefore be audible to a person situated at the oiher, 
though it may not be heard by persons placed be- 
tween these two points. The celebrated whispering 
gallery of St. Paul's cathedral in London, is an ex- 
ample. By a knowledge of this property of sound, 
the ancient priests were assisted in imposing upon 
the people their own words as the oracles of the 
gods. 

T.y the poets of antiquity, Echo was fabled as a wood nymph, who pined 
away for love, so that nothing remained of her but her voice. The grotto, 
the cavern, and the mountain side, were considered as the peculiar haunts 
of Echo. Every lover of nature is pleased in his rambles to find himself ac- 
companied by Echo, who, in softer and sweeter tones, reflects his own ac- 
cents. A great musical composer said that Echo was the best school- 
mistress ; " for, let a man's music be ever so good, by playing to her, she 
would teach him to improve it." 

490. The speaking trumpet is constructed on a well known 
principle, viz : that sound may be heightened by reflection. The 
voice, instead of being dispersed in the open air, is confined 

within a tube, and the vi- 

Fig. 174. brations falling against its 

sides, are reflected and com- 

- y bined with those which are 

"''IT.'--'-^ moving forwards, and thus 

concentrated, all move on 

to the point towards which 
the voice is directed. The lines within the tube, (Fig. 174,) re- 
present the manner in which sonorous vibrations are propagated ; 
F represents the focus, or that point in which the waves of sound 
unite and are most intense. The speaking trumpet is of great use 
at sea, enabling the commander of a vessel to make his voice 
heard amidst the " sound of many waters," and in the most vio- 
lent tempests. 

491. The ear-trumpet is wider where the sound enters, than 
where it is applied to the ear ; its sides are so curved, that, ac- 
cording to the law of reflection, all the sound which enters, is 
brought to a focus in the narrow end. The intensity of sound is 
thus greatly increased before it reaches the ear, and the deaf, by 
means of this invention, are enabled to enjoy the conversation of 
friends.* 

* It is of late found that tubes of Indian rubber answer even a better pur- 
pose than the common ear-trumpet. From the nature of this substance, 
tubes may be made of a much greater length than could be conveniently 
used, if formed of an inflexible material ; and it is ascertained, that the longer 

490. Speaking trumpet. 

491. Ear-trumpet. Shell ear-trumpet. 

16 




182 NATURAL PHILOSOPHY. 

Some sea shells, from their concave, polished surfaces, are re- 
markably adapted to collect and concentrate the waves of sound. 
When properly fitted with a small tube, a shell of this kind forms 
an elegant and useful ear-trumpet. The resonance of sound 
within a large sea shell, is often a cause of wonder to the young, 
who are ready to fancy they hear within it, the roaring of that 
distant ocean of which it was once an inhabitant. 

Velocity of Sound. 

492. Sound, though it moves with great velocity, is less rapid 
in its progress than light. The lightning is seen before the thun- 
der is heard, though the same electrical discharge is the cause of 
both. The flash of a gun is seen before the report is heard. 
The axe of the distant laborer may be seen to fall, before the 
sound of the blow is heard. 

493. It is ascertained that sound moves through the atmos- 
phere at the rate of 1142 feet (nearly a quarter of a mile) in a 
second. We may determine the distance of a thunder-cloud, 
by noticing the number of seconds which elapse between the 
lightning and the thunder. Since the pulse of a healthy person 
beats about once in a second, each pulse will indicate a distance 
of about a quarter of a mile. Thus, sixteen beats between the 
lightning and the report, would indicate a distance of about four 
miles, thirty two beats eight miles, &c. The distance of a ship 
at sea may be determined, by observing the time which passes 
between the flash of a gun fired from it, and the report of the 
same. The quickness with which an echo is returned, may also 
serve for a measure of distance. Thus, suppose a cliff upon the 
opposite bank of a river to return an echo in one second ; as 
sound travels 1142 feet in a second, the breadth of the river must 
be half this distance, or 576 feet ; since one second elapses while 
the sound is going and returning. 

# Music. 

494. The natural music of birds, and the power of singing, or 
producing agreeable notes by the human voice, led, in the course 

the conducting tube, the more intense is the sound. Thus, M. Biot, of Pans, 
found that aqueduct tubes a mile in length, conducted the most feeble sounds, 
so that according to his expression, " the only way to prevent being heard 
at the opposite extremity of the tube was not to speak at all." 

492. Sound moves with less velocity than light. 

493. Distance of a thunder cloud ascerlained by observing the time be- 
tween the lightning and thunder. Ship at sea. Echo, a measure of distance. 

494. Invention of musical instruments. 



Till] HUMAN VOICE. 183 

of ages, to the contrivance of stringed instrument 

guitar, dec. ; and to the invention of wind instrument, as the Hide, 

lilt', VN 

j!)r>. In stringed instruments, as the harp and piano-forte, the 
air is struck by the string, and the vibrations of the air produce 
a corresponding sound in the ear; but, in pipes, as in the flute 
and organ, the air is forced against the sides of the tubes by the 
breath, and its vibrations or tones are produced by the reaction of 
the sides upon the air. 

496. Sound is varied by the rapidity and momemtum of the vibra- 
ting body ; and this vibration depends on the length, tension, and 
size of the string. A short string vibrates more quickly than a long 
one, and therefore produces the sharpest and highest tones ; and a 
short and small pipe, from alike cause, produces sharp tones; 
and large pipes, grave and deep sounds. Savages early discovered 
this ; and they made, and still make, simple instruments which 
please themselves and their wild companions. But art and sci- 
ence go further; they ascertain the causes of the pleasure derived 
from musical sounds, and thus proceed to complex inventions, in 
order to afford a higher gratification. 

497. When an agreeable succession of simple notes having a 
perfect beginning and ending, is played or sung, the effect is call- 
ed an air, or melody. When these notes forming an air, are- 
combined with corresponding notes, indifferent octaves or on other 
instruments, and the whole is scientifically made to produce a con- 
cordant and agreeable effect, this is called harmony. The bass 
and treble of a piano-forte, played at the same time with the left 
and right hand, constitute the most common instance of harmony. 
Some of Handel's pieces have been played by 1000 instruments 
and voices, all sounding harmoniously together. 

The Human Voice. 

498. Ancient physiologists considered the windpipe* as the im- 
mediate organ of sound, and that the voice was caused by the 
action of air against its sides, as sound is produced in musical 
pipes. But the ancients erroneously imagined this action of the 
air to be produced as it w^as passing into the lungs, or in the in- 
spiration of the bre&th ; whereas, it is now understood that the 
voice is formed during the expiration of air, or in its passage yrom 

* Technically called the trachea. 

495. Difference in stringed instruments and pipes. 

496. Cause of the variety of sounds. 

497. Melody and harmony. 

498. Opinion of the ancients respecting the human voice. Their error. 
Office of the lunsrs. 



184 NATURAL PHILOSOPHY. 

the lungs. The lungs may be considered as performing the same 
office in propelling air into the windpipe, as the bellows of an 
organ in blowing air into the pipes of that instrument. 

499. The organs which are essential to the production of vo- 
cal sound, are the lungs, windpipe, larynx, and glottis. Respect- 
ing the action of the lungs, and the effect of air upon them, we 
have previously made some remarks.* The wind or air pipe, is 
a cartilaginous tube, through which the air passes to and from the 
lungs ; the larynx is an enlargement of the windpipe situated at 
the back of the mouth. Just below the larynx, is the glottis, a 
smaller passage furnished with muscles for contracting, enlarg- 
ing, or altering its form, so as to produce a great variety of sounds. 
Indeed, it is principally to the powers of this small organ, that 
we attribute the phenomena of vocal sounds. If the windpipe 
below the glottis is perforated, so that the air, in expiration, issues 
at the orifice, there is no vocal power ; but it is otherwise with 
an injury to the throat which does not affect the glottis. 

500. Naturalists say, that even the windpipe and larynx may 
be taken from an animal without destroying its voice. Baron 
Cuvier asserts, that having cut off the head of a bird without in- 
juring the glottis, the headless animal uttered several cries. — 
Some curious naturalists have experimented with the vocal organs 
of a pig, by fitting to the windpipe the bellows of an organ 
which answered the purpose of the lungs, and varying the aper- 
ture of the glottis by pressure with the fingers, have succeeded in 
imitating, with this apparatus, the grunting sound peculiar to that 
animal. 

501. By observing the formation of the vocal organs in man, 
mechanicians have succeeded in constructing instruments which 
articulate letters, and even words and sentences. A German, 
who made himself famous for the invention of an automaton 
chess-player, is said to have succeeded in constructing a speaking 
machine which can talk in French and Latin. It is gravely sug- 
gested by some men of science, that from the discoveries made of 
the mechanism of the vocal organs and the nature of the human 
voice, it may be possible to construct machines for the pronunci- 
ation of modern languages, so that our language may be trans- 
mitted to the ear as well as to the eye of future generations. 

502. But with all man's invention, he can never make a living, 
breathing, thinking, or talking machine. The greatest efforts of 

* See Pneumatics, $ 396. 

499. Organs of sound. 

500. Experiments with the vocal organs of animals. 

501. Speaking machines. 

502. Limited power of man. 



LIMITED l'OWEli OF MAN. 185 

human ingenuity, when compared with the productions of nature, 
an* as ihf rude attempts of an unskilful hand in touching a mu- 
sical instrument, to the perfection of a finished performer, who 
knows the exact powers of every key, and how to mingle sounds 
to produce a varied and melodious harmony. The imbecility of 
man must ever appear, when he directs his efforts into the region 
where God works, when he attempts to produce phenomena 
analogous to those of life. Man may copy, but God only can 
create. 

16* 



PART VI 

OPTICS. 



LECTURE XXti. 



LIGHT. DEFINITIONS. MOTION OF LIGHT. ITS INTENSITY. 

OF REFLECTION, AND REFRACTION. 

Preliminary Remarks on Light. 

503. The science which treats of light and its effects is called 
optics. This term is from the Greek, and signifies " relating to 
sight ;" — the word optics signifies an organ of sight or vision. 

504. So important is vision to man, that, as we should natu- 
rally expect, light and its phenomena early received the attention 
of philosophers. The science of optics is among the oldest 
branches of Natural Philosophy. Some of its most important 
principles were suggested by Plato and Aristotle. To the mod- 
erns, however, we are indebted for the invention of many of the 
most valuable optical instruments. 

Philosophers have investigated the nature and effects of light, 
and poets have sung of its glories, but the enlightened christian, 
to philosophy and poetry, adds the homage of a devout and pious 
heart. He considers whose spirit it was that moved upon the 
dark and formless void ; — who said " let there be light," and who, 
in view of the comfort and enjoyment it would bestow on his cre- 
ation, pronounced this light to be "good." 

505. The nature of light is not known. It is generally be- 
lieved to be matter, since, in its motions, it obeys the laws which 

503. Definition of optics. 

504. Antiquity of the science of optics. Reflections. 

505. Nature of light. Newton's hypothesis respecting the nature of light. 
Hypothesis of Euler and others; 



DEFINITIONS. 187 

govern matter. Light is closely connected with heat and electricity, 
and there are some reasons for the belief that the three substan- 
ces are but different modifications of the same principle. 

Sir Isaac Newton supposed rays of light to consist of minute particles of 
mutter, which arc constantly emanating from luminous bodies, and cause 
vision ; as orodiferous particles, proceeding from certain bodies, cause smell- 
ing. This is called the system ot emanation. Some philosophers affirm that 
light is nothing more than the agitation of a medium called ether, which is 
far lighter and more subtile than air. They suppose that rays of light are 
produced by vibrations of-air. One of the most celebrated advocates of the 
theory of undulations and vibrations, is Euler, who flourished in Germany, 
in the eighteenth century. But the beginner in science would profit little 
by attempting to enter a field of controversy, in which the greatest philoso- 
phers have found themselves wandering blindfold among luminous and 
opaque bodies, searching for light, but finding none. It is here as in other 
departments ef science, if we limit our inquiries to the powers and qualities 
of bodies, we find our toil amply rewarded; but if we attempt to lift the 
veil which God has interposed between us and the secret elements of which 
he formed matter, wo find our grasp eluded, and our search confounded. 

506. It is not the absolute nature of light which we are to in- 
vestigate, but the effects of light upon other bodies, and how 
light is affected by them. To assist in determining how light 
affects other bodies, let us for one moment close our eyes ; the 
instant void which succeeds, proves what would be the conse- 
quences of the absence of light ; — we open our eyes and innu- 
merable objects present themselves. The beauty and sublimity 
of nature, in its endless variety of form and color, would, but for 
the agency of light, exist for man in vain. 

The manner in which light is affected by other bodies, involves 
some of the most important principles in optics, as reflection and 
refraction. 

Definitions. 

507. Luminous bodies are of two kinds ; those which shine by 
their own light, as the sun, a lamp, or fire ; and those which shine 
by reflected light, as the moon. 

Transparent or diaphanous* bodies are such as permit rays of 
light to pass through them. A perfectly transparent body is in- 
visible. Air, when free from vapor of all kinds, is invisible. 
Water is not perfectly transparent, since it is visible, which is also 
the case with the clearest glass or gem. Translucent bodies 
permit light to pass faintly, but without representing the figure of 
objects seen through them, as China ware, and alabaster. 

* From the Greek, diaphanes, signifying shining through 

506. What are we to investigate in regard to light? How light affects 
other bodies, &c. 

507. Luminous bodies. Transparent bodies. Translucent bodies. Opaque 
bodies. 



188 NATUEAL PHILOSOPHY. 

Opaque bodies permit no light to pass through them, as wood, 
stone, &c. Such bodies reflect light, and by this means, not only 
render themselves visible, but diffuse light from luminous bodies 
around them, as the moon and planets. 

508. A ray is a line of light. A beam is a collection of paral- 
lel rays. A pencil is a collection of converging, or diverging 
rays. A medium is any space through which light passes. A 
perfect vacuum is said to be a free medium. Air and glass are 
transparent mediums.* 

Parallel rays are such as proceed equally distant from each 
other, through their whole course. Converging rays are such, as 
proceeding from any body, approach and tend to unite in a point 
in the form of a cone. Diverging rays are those which, proceed- 
ing from a point, continue to recede from each other, in the form 
of an inverted cone. A focus is that point at which converging 
rays meet. 

Motion of Light. 

509. 1st. Light moves in straight or right lines. Rays of 
light are projected from a luminous body in every direction, but 
always in right lines ; these lines cross each other at every point, 
but the particles of which each ray consists, are so minute that 
the rays do not appear to be the least impeded by each other. 
Wherever a spectator is placed with respect to a luminious body, 
every point of that part of the surface which is turned towards 
him is visible ; this shows that the light is emitted in all direc- 
tions. A ray of light passing through an aperture into a dark 
room, proceeds in a straight line. We can see objects through 
a straight tube, though not through a curved one ; but we can hear 
through a bent tube, which proves, that the radiation of light is not 
governed by the same laws as that of sound. Because light 
moves in straight lines, if a number of objects of the same height 
be placed in a row from the eye, the nearest one hides the others ; 
as, for example, a row of trees, or a line of soldiers. 

510. 2d. Light moves with great velocity. When a gun is fired, 
we see the flash before we hear the report, and lightning ,pre- 

* The plural of medium, according to the Latin construction, is media, but 
when used in English, it seems proper to adopt the form of plural most com- 
mon in our language. 

508. A ray. A beam A pencil. A medium. Parallel rays. Converg- 
ing rays. Diverging rays. Focus. 

509. How does light move ? Radiation of light not governed by the same 
laws as that of sound. 

510. Velocity of light compared with that of sound. Velocity of light cal 
culated by means of the eclipses of Jupiter's satellites. 



INTENSITY OF LIGHT. 



189 



Fig. 175. 



cedes the thunder; these facts prove that light moves with great- 
er velocity than sound. Astronomy has enabled men not only to 
foretell eclipses of the heavenly bodies, but, by means of these 
eclipses, to ascertain the rate at which light travels. 

The rate at which liyht is propagated was discovered by Olaus Roemur, 
fa making observations on the eclipses of the satellites of Jupiter. If the 
transmission of light were instantaneous, it must be obvious that the reflected 
light of the *un would take up no more time in passing from any of the plan- 
etary bodies to the earth, when they are farthest from us, than it does when 
they are nearesl ; and as the situation of the earth, with respect to the other 
is different in different parts of her orbit, the satellites of Jupiter in 
emerging from the shadow of that planet, would be seen as quickly when 
the earth was in one part of her orbit, as in another. The planet Jupiter has 
four moons, which revolve about him as our moon revolves about the earth; 
thev are subject to frequent eclipses, and from the same cause as that which 
produces eclipses of our moon, viz., the entering of the satellite into the 
shadow made by the primary; or, in other words, by the primary planet 
interposing between the satellite and the sun. By means of the telescope, 
an eclipse of one of Jupiter's satellites may be observed, with the time of its 
entering and emerging from the shadow cast by the planet. Astronomers 
calculate the exact moment of these changes as if 
viewed from the sun, S. But the earth and Ju- 
piter are sometimes on the same side of the sun, 
and sometimes on opposite sides ; in the latter 
case, the earth is farther from Jupiter by the whole 
diameter of its orbit, (or 190,000,000 of miles,) 
than when the two planets are on the same side 
of the sun. It is found by observation, that when 
the earth is nearest to Jupiter, an eclipse of one 
of his satellites is seen sooner, than when the earth 
is at its greatest distance from that planet. Let S 
represent the sun, A and B the earth in different 
parts of her orbit, d Jupiter, D his nearast satel- 
lite entering the shadow of that planet, and C the 
same satellite emerging from the shadow. When 
the earth is at A, the eclipse takes place about 8 
minutes earlier than the calculated period, and 
when at the part of her orbit B, or most distant 
from the planet Jupiter, about 8 minutes later; 
that is, about 16 minutes of time elapse while light 
is traveling across the earth's orbit, 190,000,000 
of miles, or from A to B. By an arithmetical cal- 
culation, we find, if light travels a distance of one 
hundred and ninety millions of miles in 16 minutes, it moves at the rate of 
about 197,916 miles in one second.* 

Intensity of Light. 

511. Light diffused by a luminous body becomes fainter, as the 
squares of the distance increase. Suppose before the candle «, 
are placed three square boards, b, containing 1 square inch, c 4 

* 190,000,000^-16X60 = 197,916. 




511. Efl< 
of light. 



ice upon light. Rule of calculating the diminution 



190 



NATURAL PHILOSOPHY. 

Fig. 176. 




square inches, and d 16 square inches. Let b be placed at the 
distance of 1 foot from the candle, c 2 feet, and d 4 feet. Here 
the smallest board b, will obstruct all the rays of light which 
would otherwise fall on c ; and if b were removed, c would in 
like manner hide the light from d ; now if the first board receive as 
much light as would fall on the second, whose surface is four 
times as large, the light must be four times as powerful, and six- 
teen times as powerful as that which would fall on the last board, 
because the same quantity of light is diffused over a space six- 
teen times greater. The light of a candle can be perceived, in 
a clear night, at the distance of one or two miles, if not ob- 
structed by intervening objects. As sound within a certain dis- 
tance dies away, and is lost in silence, so light insensibly fades 
into darkness. 

Of Refection, and Refraction. 

512. The term refection, as used in optics, signifies the re- 
bounding of light from surfaces on which it falls. Here we see 
light following exactly the same laws as is common to all matter ; 
thus affording a proof that it is, itself, a material agent. All 
bodies do not reflect light ; it is only polished surfaces which 
have this property, and of such surfaces, some, as diamonds 
and glass may transmit, without reflecting light. Mirrors de- 
rive from reflection, their property of throwing back the image 
of an object. 

513. Refraction* denotes the bending of the rays of light, as 
they pass from the surface of one transparent medium to another. 
Thus, in passing from air into glass, all the rays, except those 
that fall perpendicularly, are turned from their straight course, 
or refracted. To the refraction of light we are indebted for the 
power of the lenses, or magnifying glasses, used in the manufac- 
ture of spectacles, telescopes, and microscopes. It is to the re- 

* Refraction is so called from the Latin prefix, re, and frango, to break, on 
account of the. broken appearance of a ray of light. 



512. Reflection. 

513. Refraction. 



Surfaces which reflect light. 



ANGLES OF INCIDENCE AND REFLECTION. 191 

fraction of light by the different lenses of the eye, that this or- 
gan owes its power of seeing.* 

514. Inflection,] signifies the turning of rays of light from their course, by 
the attraction of opaque bodies. If a beam of light be admitted through a 
small aperture into a dark room, and the edge of a knife be brought near the 
beam, the rays of light, which would, otherwise, have proceeded in a straight 
line, will be inflected, or turned towards the knife. On placing the edge of 
another knife very near to that of the former, the stream of light divides in 
the middle and leaves a black stripe, indicating that all the light has been 
attracted from that space towards the two edges. As the knives are brought 
nearer to each other, the dark stripe widens, till, upon the contact of the 
knives, the whole light vanishes. Fringes of different colored light appear 
on the edges of the two knives, three separate fringes on each, and all vary- 
ing in their colors; the first fringe beginning with violet and terminating 
with red, the second beginning with deep blue and terminating with red, 
the third beginning with pale blue and terminating with pale red. As the 
separation of light in the rain-bow, is the effect of refraction, we may con- 
clude that by inflection, the different colored rays being differently acted 
upon, a similar decomposition of light is produced. When we look at a 
candle with the eyes almost closed, fringes of light appear; the eyelids will 
in this case, cause the inflection of the beams of light which enter them. 

Thus we find that light may suffer a change of direction without actually 
infringing on a body, but merely by coming within the sphere of its irjjlvence ; 
as one body gravitates towards another, as the needle is attracted by the 
magnet, and as one body in a different electrical state from another, is drawn 
towards it. 

The inflection of light is rather to be regarded as a curious optical phe- 
nomenon, than studied in relation to its bearing upon any known laws, or 
important applications of science ; but reflection and refraction are subjects 
which must be attentively studied as the two fundamental principles of 
optics. 



LECTURE XXXII. 

REFLECTION FROM MIRRORS. PLANE MIRRORS. CONVEX 

MIRRORS. CONCAVE MIRRORS. 

Angles of Incidence and Reflection. 

515. A ray of light turned back into the same medium through 
which it fell, is said to be reflected. 

* Though in accordance with the common use of language, we say, the 
eye sets, it should be understood that the seeing is, in reality, in the mind, 
to which the eyes serve as spectacles. 

t From the Latin verb inflecto, to crook, or bend in. 



514. Inflection. Light influenced by attraction. 

515. What is a reflected ray ? 




192 NATURAL PHILOSOPHY. 

516. Incident * rays, are those which fall on the surface of a 
body ; reflected rays, are those which are thrown from it. When 
a ray of light falls perpendicularly on an opaque body, it is re- 
flected in the same line in which it proceeded ; in this case, the 
reflected ray returns in the same path as that in which the 
incident ray went. But when a ray falls obliquely, it is re- 
fleeted obliquely ; that is, the reflected ray proceeds in a line on 
the oppositite side, as far from the perpendicular, as was the 
incident ray. The angle made by the incident ray, at the sur- 
face of the reflector, with a line perpendicular to that surface, 
is called the angle of incidence ; the angle made by the reflect- 
ed ray, with the same perpendicular line, is called the angle of 
reflection. 

Suppose A B to represent a reflecting sur- 
Fig. 177. face, C D, a perpendicular to this surface, E 

D the incident, and F D the reflected ray, 
the angle E D C is the angle of incidence, the 
angle FDC is the angle of reflection, and 
the angles of incidence and reflection are equal. 
Let a circle be described around the point D 
as a center ; taking D E and D F for radii, it 
will be found that equal portions of circumference lie between 
E C and C F ; this proves that the angles E D C and F D C 
are equal. And, again, since A D C is a quadrant, equally di- 
vided by the line E D, and B D C is a quadrant equally divided 
by F D, it follows that the angle A D E is equal to D B F, and 
the angle E D C is equal to F D C. 



Reflection makes objects visible. 

517. It is by the reflection of light that objects are made visi 
ble ; while light itself, unless it fall directly upon the eye, is in- j 
visible. If a room be closed so that it is dark, except as a beam 
of light entering through a hole in the window- shutter gives a 
partial illumination, a bright spot may be seen on the wall oppo- 
site, and the course of the rays of light may be traced by means 
of the motes or small particles of dust floating in the air. Thus \ 
the agent which enables us to see all other things, remains itself j 
unseen, and, like its great Creator, is known to us only by its 1 
effects. 

* From the Latin incido, to fall upon. 
. 

516. What are incident rays ? How is a ray falling perpendicularly re- 
flected ? A ray falling obliquely. Angles of incidence and reflection. 
Equality of the angles of incidence and reflection. 

517, Objects made visible only by the reflection of light. 



PLANE MIRRORS. 193 

The eye, itself, is not made sensible of the presence of light, 
till, after a certain series of operations upon its various coverings 
and humors, seeing is produced. 

518. Smooth and polished surfaces reflect light most power- 
fully, producing, upon the eye, the images of the objects from 
which the light proceeded. Glass, which is transparent, or, in 
other words, transmits rays of light, by being rendered opaque, 
is made to reflect them. This is done by a metallic covering call- 
ed an amalgam applied to one side. This amalgam interrupts the 
light in its passage from the glass into the air, turns back the 
rays, and throws them either directly in the incident line, or in an 
oblique direction. The reason why trees, rocks, and men are 
not all mirrors, reflecting other forms instead of their own, is that 
their surfaces are uneven. — Rays of light reflected from uneven 

surfaces are diffused in all directions. 
The parallel, horizontal lines in Fig. 
178 represent the sun's rays, which 
striking upon the angular surfaces 
of the body a 6, are diffused, as 
seen in the lines which cross the 
horizontal lines. If the reflecting 
surface be polished, although un- 
even it will be very brilliant, as in 
crystals, diamonds, and cut glass. — 
Here the effect is produced by the 
reflection of light from numerous 
polished angles. 

Mirrors. 

519. A Mirror is a smooth surface which reflects light. Thus 
a still lake, a polished plate of metal, and a looking glass, are 
mirrors. That department of optics which treats of the reflec- 
tion of light by means of mirrors, is called Catoptrics.* 

Mirrors are of three kinds, the plane, convex, and concave. 
A plane mirror is flat, or has its surface a perfect plane as in 
common looking-glass. A convex mirror is globular, and re- 
flects images from a rounded surface. A concave mirror is cur- 
ved inward, and reflects light from a hollow surface. 

* From the Greek kataptron, a mirror. 




518. Surfaces which reflect light most powerfully. Light reflected from 
uneven surfaces. 

519. A mirror ? What is Catoptrics ? Different kinds of mirrors. 

17 



194 



NATURAL PHILOSOPHY. 



The Plane Mirror. 
520. A common looking-glass is a plane mirror, composed of 
glass rendered opaque by a coating of tin and mercury. The 
rays of light having passed through the glass, are thrown back 
by the metallic surface ; the glass is only necessary for preserv- 
this surface smooth and clear. Rays of light in passing through 
the glass, suffer some degree of refraction, and thus give a less 
perfect image than a pure, metallic reflector. For this reason, 
such mirrors are used in many optical glasses. The term spec- 
ulum refers to a reflector which is metallic, or made of silver, 

tin, &c. ; Mirrors are also called 
specula. 

521. Parallel rays falling oblique- 
ly on a plane mirror are reflect- 
ed parallel; — the rays d 6, and 
c a, which are parallel, are re- 
flected in parallel lines towards h 
and k. 

522. Converging rays are re- 
flected from a plane mirror with 
the same degree of convergence ; 
d b and c a are convergent, and 
without the interposition of the 
mirror, they would unite in the 
point E ; but being reflected, they 
unite in the opposite point F. 

523. Diverging rays reflect- 
ed from a plane mirrors equal- 
ly divergent ; d b and c a are 
divergent rays ; if they had 
proceeded without interruption 
from the mirror, they would 
not have united at any point 
beyond it, as may be seen at 
E and F, because the tendency 
of divergent rays is to depart 
still farther from each other ; 
falling upon the surface of the 
mirror, they are reflected to- 
wards, h and k, the lines of 
reflection being equally diver- 
gent with the lines of incidence. 




520. Common looking-glass. Speculum. 

521. Parallel rays falling obliquely on a plane mirror. 

522. Converging rays reflected from a plane mirror. 

523. Diverging rays reflected from a plane mirror. 



PLANE MIRRORS. 



195 



Fig. 182 




524. When an object is placed before a plane mirror an image 
is formed, which appears to be, as far behind the mirror, as 
the real object is before it. 

Suppose M R to be a marble slab, an 
elastic ball thrown from A, perpendicularly 
towards it at D, would rebound in the same 
line to A ; but if thrown obliquely, as from 
B to D, it would move off to b, as far on 
the opposite side of the perpendicular, mak- 
ing the angle of reflection equal to the angle 
of incidence ; if thrown from C, it would 
be reflected to c ; and from any other point, 
the same law would govern the reflection. 
But suppose M R a plane mirror, and light 
to pass from an eye situated at A ; the eye would see itself as if 
behind the mirror at d ; or an eye at b would see an object situa- 
ted at B as if it were at e ; or an eye at c would see an object at 
C as if it were at f. The incident ray A D, and the reflected 
ray D d, or the incident ray A, and the reflected ray D e, form 
together what is called the passage of reflection, and this will, 
therefore, make the real distance of an image seen in the plane 
mirror, appear as far again from the eye as it really is ; or, in 
other words, the image will appear as far behind the mirror, as 
the real object is beibre it. A person standing before a looking- 
glass, sees his figure as if behind the glass ; if he walks towards the 
glass, the image will approach, but with double the real velocity, 
because both the incident and reflected rays are contracted by 
the movement. If he walks from the glass, the image seems to 
retire from him, with double his own speed. 

525. Suppose an object A to be so situated in 
respect to the mirror M N, that the ray A B fall- 
ing upon the mirror, is reflected to the line B C ; 
let a perpendicular line be drawn from A to a, 
and extend the reflected ray B C, till it cuts the 
perpendicular at a, the distance a S is equal to 
S A, also every other ray proceeding from the 
object A will be reflected as if coming from be- 
hind the mirror at a. To an eye at O, the image 
a would appear as far behind the mirror, as the 
object A is before it. 

526. An object which reflects light, is 
called a radiant ; this radiant is, therefore, 
the point from which rays diverge, or the 




524. Apparent situation of the image formed by reflection from a plane 
mirror. Passage of reflection. 

525. Why does the image seem to move with double velocity when a 
person approaches or recedes from a mirror? 

§26. Focus of divergent rays. Virtual focus* 



196 



NATURAL PHILOSOPHY, 



focus of divergent rays, and the point behind a reflecting surface 
from which they appear to diverge, is called the virtual focus. 

527. Since rays of light are reflected at the same angle as that 
at which they strike a reflecting surface, two persons may stand 

in such positions, that each can see 
Fig. 184. the image of the other, in a mir- 

ror, without seeing his own. Sup- 
pose M N, to represent a mirror, A 
and B the positions of two persons 
with regard to it ; the line P C is a 
perpendicular drawn from the surface 
of the glass at the point P, where the 
rays from A and B fall upon the mir- 
ror. The person at A, looking to- 
wards the mirror, would not see his 
own image, but that of him who 
stood at B, which would appear as if 
behind the mirror at b ; in the same 
manner B would see A, as if stand- 
ing at, a. 

528. A person may see the whole of his figure in a plane mir. 




ror which is but half his height. 
Fig. 185. 




Suppose B D to be a 
mirror half as high as the 
figure A C ; the ray of 
light, A B, from the eye, 
falling perpendicularly on 
the mirror, is reflected 
back in the same line but 
the ray C D, from the foot, 
which falls obliquely, is 
reflected in the line D A. 
Since we view objects in the direction of the reflected rays which 
meet the eye, and as the image appears at the same distance be- 
hind the mirror that the real object is before it, the line A D 
must be extended to E, and the line C D to F, and here the image 
will appear to be situated. 

But if the mirror is less than half the height of the figure, the 
whole of the figure cannot be reflected. Thus it may be seen in 
Fig. 185, that were the mirror only of the height of O B, the 
line C O from the foot of the figure, would be reflected in the line 
O F, above the eye. 

527. In what position may two persons see each the image of the other in 
a mirror without seeing his own ? 

528. How may one see an image of his whole figure in a mirror but half 
' Suppose the mirror to be less than half the height of the figure 




CONVEX HIBH0B8. 197 

529. An object viewed in a mirror appears reversed ; thus the 
left loot of the figure A C, (see Fig. 185,) or the one which 
seems stepping forward, appears the right foot in the image F 
E ; and when we stretch out our right hand, to take that of the 
image in a mirror, the latter seems to offer a left hand. By 

holding written or printed charac- 
Fig. 180. ters before a mirror, we perceive the 

effect of this reversion, in changing 
the image of objects from right to 
left. In the human figure there is, 
generally, great uniformity ; the fea- 
tures on one side of the face being 
usually a very exact representation of 
those on the other ; but where there 
is any peculiarity, as the nose a little 
turned to one side, or a squint eye, a 
man who should undertake to paint his own portrait would be in 
danger of reversing these traits, and making a caricature instead 
of a likeness. By reflecting an image from one mirror to another, 
the last reflection presents the object without being reversed, and 
written or printed characters appear as when seen without any 
reflection. 

Convex Mirrors. 

530. Convex mirrors reflect light from a rounded surface, as 

A B. Any polished, convex body is a mirror, 
Fig. 187. as the spherical part of brass andirons with 

which children often amuse themselves in view- 
ing their own miniature likenesses. The hu- 
man eye is the most perfect of all convex mir- 
rors, and so great is its power of diminishing 
objects and yet preserving their exact like- 
nesses, that on a surface of less than half an inch in diameter, may, 
be represented a landscape, where men, animals, buildings, dis- 
tant fields and hills, with mountains and clouds, are distinctly de- 
lineated. 

531. Convex mirrors disperse rays of light; — they cause par- 
allel rays to diverge, converging rays to converge less, and diverg- 
ing rays to diverge more. 

529. Image of objects seen in a reversed position. 

530. What is a convex mirror ? The most perfect convex mirror. 

531. How do convex mirrors reflect rays of-light? How does the figure 
illustrate this subject ? What is the axis of a convex mirror ? 

17* 



198 



NATURAL PHILOSOPHY. 



Fig. 188. 




Let M N be a convex mirror, A M, A D and A N parallel 
rays falling upon it ; if the mirror were flat, the rays would 
all be perpendicular to it, but as it is spherical, no ray can 
be perpendicular to it, which is not directed towards C, the 
center of the sphere. The ray A D is perpendicular to the 
supposed center, of which the convex mirror forms a part. 
Therefore A D, which falls perpendicularly, is reflected in 
the same line. But A M and A N, which fall obliquely, 
are reflected obliquely, in the direction M B and N B. The 
lines C E, which meet in the center of the sphere, and are 
therefore perpendicular to it, divide the angles of incidence and 
reflection, which may be seen to be equal. The image will be 
seen as at F, which is the point where the reflected rays, if con- 
tinued through the mirror, would unite. This point, which is 
equally distant from the surface and center of the sphere, is called 
the virtual or imaginary focus. 

The axis of a convex mirror, is a line passing through its center, 
as A C. (See Fig. 188.) 

532. All spherical mirrors are curvilinear, 
that is, they are arcs, or segments of circles. 
Curves are formed of a number of straight lines, 
or points, infinitely short, and inclining to each 
other, like the stones in the arch of a bridge. 
Each of these points may be considered as a 
plane mirror, and the whole convex surface as 
consisting of innumerable small, plane mirrors, placed at angles 
with respect to each other, but forming a curve in their general 
arrangement. Such rays only as fall perpendicularly upon the 



Fig. 189. 




532. Spherical mirrors curvilinear. 



CONVEX MI11RORS. 



199 



convex surface, or are directed towards its supposed center, will 
be reflected back in the same direction ; all other parallel rays 
will tall obliquely upon it, and be reflected obliquely, according to 
the genera] law of reflection. 

533. Suppose the rays a b, and c d, to be parallel, yet falling on the convex 
pnfac* d b, they are, from their different points of incidence, rendered divergent 
in // and r, the angle of reflection with respect to each, being equal to the 
angle of incidence. Thus we see that convex mirrors render parallel rays 
divergent 

Fig. 190. Fig. 191. 

W 





534. Again, suppose the rays a b and c d to be convergent ; without the in- 
terposition of the reflector b d, they would unite at m, but they now proceed to 
unite in I, which is more distant from the reflecting surface than the point m. 
Here we see that convex mirrors cause converging rays to converge less. 

535. Again, the diverging rays a b, and 
c d, which, without the interposition of the 
convex surface b d, would diverge but little 
at m, become, after reflection, much more 
divergent, as may be seen in the space I ; 
and the angles of reflection will be found, 
in all these cases, exactly equal to the an- 
gles of incidence, if measured from the re- 
flecting surface produced or lengthened, as 
at/g - and i k. 

536. Convex mirrors represent objects 
smaller than they really are. This is 
because the angle formed by the reflected 
ray, called the visual angle, is rendered 
more acute by a convex, than by a plane 
surface. Suppose the object C D placed 
before the convex mirror a b ; the two rays 
C e and D d, which proceed from the ex- 
tremities of the object, and which, if not in- 

533. How can you prove that convex mirrors render parallel rays di- 
vergent ? 

534. Illustrate the proposition that convex mirrors render converging rays 
less convergent. 

535. Diverging rays falling on a convex surface. 

536. Why do convex mirrors represent objects smaller than they are in 
reality. 




200 



NATURAL PHILOSOPHY. 

Fig. 193. 




terrupted by the mirror, would converge at/, are reflected less convergent, and 
unite at i, forming an angle more acute than if they had not been reflected. 

Again, objects appear less in a convex mirror, than in a common looking- 
glass, or plane mirror, because the convex surface reflects rays from points 
nearer to each other: " ^Suppose the straight line b d to be a common mirror 
and a r the object to be viewed ; the ray from the point a, will be reflected to 
the eye situated at e from p, and the ray from r will be reflected from q ; 4 he 
image will appear at I M of the same size as the object would appear if viewed 
from the other side of the glass at o, because the angle p e q and the angle poq 

Fig. 194. 




ji*f3=^2 





are equal. But when the same object is reflected from a convex surface, re- 
presented by the curved line, the reflections, from the top and bottom will 
take place from points nearer than before, viz., from n to s. The image is 
therefore reflected from the reduced space of n s instead of p q, and it will ap- 
pear consequently, less than the object, as at i m. The angle subtended to the 
eye, by the reflection from the convex surface, is much less than that of the re- 
flection from the plane mirror, and the difference in apparent size, of the two 
reflections will bear the same proportion as the space between p q bears to the 
space between n s." 

537. 1st. As the visual angle is diminished by distance, the farther an ob- 
ject is removed from a convex mirror, the smaller is the image reflected by it 

2d. Since the different points of an object are not equally distant from the 
surface of a convex mirror, the image will appear curved. 

3d. As convex mirrors cause rays of light to diverge, images appear nearer 
the surface of such reflectors than of plane mirrors. 

* Bakewell's Philosophy. 

537. Enumerate three important laws with respect to images formed by 
convex mirrors. Explain Figure 195. 



CONCAVE MlllllOKS. 



201 



Fig. 195. 



Let A B be an object placed be- 
fore the convex mirror M N, in such 
B position that a reflected ray may 
enter tho eye placed at H. From C 
draw C A, and C 13, intersecting th i 
minor in E and F. The rays A F 
and A G, will be roflected to II and 
K, and will therefore enter the eyo 
as if they came from a, at the point 
where the perpendicular A C, is in- 
tersected by the lines from F and G. 
Likewiso 13 / and 13 g falling upon 
the points / g, will be reflected to the 
eye as if they came from b, the point 
where they intersect the perpendicu- 
lar B C. The rays being thus ren- 
dered more divergent by reflection, 
they appear to come from a b nearer 
to the mirror, than A B, and since 
the extreme points a and b are nearer 
to each other than A B, the image 
will be represented of less size. 
The greater the convexity of a reflector, the more will the images of objects 
| be diminished, and the nearer will they appear to the surface. 

Concave Mirrors, 




Fig. 196. 



538. Concave mirrors reflect light from a hollow sur- 
face, as E F. The concave mirror being, in form, 
the reverse of the convex, we find its powers essential- 
ly different, Concave mirrors, collect rays of light 
and magnify objects, while convex mirrors, disperse 
rays of light and diminish objects ; plane mirrors re- 
flect rays of light, without either enlarging or dimin- 
ishing the visual angle, and consequently represent 
objects of their natural size. 

539. Concave mirrors render rays of light more con- 
vergent. 

The surface of a concave, like that of a convex 
mirror, may be considered as composed of numbers 
of points, or small plane mirrors ; but, in the concave, 
these points are inclined towards each other, while in 
the convex, they lean in the contrary direction. Thus 
let A B, be one section of a concave mirror, and c and d 
parallel rays falling upon points on its surface ; instead 
of being reflected parallel, as in the case of a plane mir- 
ror, or divergent as in a convex mirror, they converge 
and meet in the focus e, as they would do in the case 
of two plane mirrors leaning towards each other and 
meeting in the point o. 

538. Concave and convex mirrors. 

539. How is it proved that concave mirrors render rays of light morecon- 




202 



NATURAL PHILOSOPHY. 



Fig. 198. 




a 



1 



B \ 



Fig. 199. 



.?-. 



540. Let A B represent a con- 
cave mirror, C is the center of 
concavity, or the center of the 
sphere of which the mirror is a 
section. The line FCc passing 
through its center is the axis of the 
mirror. F, is the focus of parallel 
a rays ; or that point before the mir- 
^ ror, where the parallel rays a b 
c d and e being reflected, meet. 
This focus is situated half way be- 
tween the surface of the mirror S, 
and the center of concavity, C. 
541. Again, let G M represent a concave 
mirror, C being the center of concavity ; the 
parallel rays f G and / M will pass to the 
other side of the perpendiculars C G and C M, 
and meet at the focus of parallel rays F. 

But when the incident rays are divergent, 
the focus is removed farther from the surface 
of the mirror. If they diverge from a point- 
more remote than the center, as A G and A M, 
making a less angle with the perpendiculars 
than the parallel rays make, they will also 
make a less angle on the other side of the 
perpendiculars, and meet in the point a be- 
tween the focus and center. If rays diverge 
from the center, as C G, C O and C M, they 
will be reflected back to the same point C, 
because they are all perpendicular to the 
center. Rays which diverge from a point 
between the center and a focus, as from a, 
converge to a point V, on the other side of the 
center. Rays diverging from the focus F 
are reflected parallel asG/ and M /. 

Rays that approach the mirror converging 
as d G and d M, meet in a point between the 
focus and the mirror, as at D, they are reflect- 
ed in the lines G d and M d, appearing to proceed from the point V behind the 
mirror, which point is called the virtual or imaginary focus. 

542. " One who looks into a concave mirror sees his own face varied in the 
following manner. When he holds the reflector near his face, he sees his im- 
age distinct, because the rays come to the eye diverging (which is their natu- 
ral state with respect to near objects) and enlarged, because as the rays di- 
verge less than before, the image is thrown back to a greater distance behind 
the mirror, than the object is before it, and the magnitude is proportioned to that 
distance. As he withdraws the eye, the image grows larger, and larger until 
the eye reaches the focus. From the focus to the center no distinct image is 




540. Show by the figure the center of concavity, &c. of a concave mirror. 
5<11. What is proved by Fig. 199? 

542. How may a person, viewing his image in a concave mirror, vary this 
image by a change of position ? 



CONCAVE MIRRORS. 203 

i , because the rays come to the eye converging, a condition incompatible 
with distinct vision. At the center, the eye sees only its own image, since the 
image is reflected back to the object, and coincides with it. Beyond the cen- 
ter, his fiuM will be seen on the other side of the center before the mirror, 
(though habit may lead him to refer it to a point behind it,) and it will be di- 
minished, being nearer to the mirror than the object is, and inverted, because 
an inverted image is formed when the rays are brought to a focus, and this be 
comes the object which is seen by the eye."* 

543. The sun's rays, on account of the vast distance of that 
body from the earth, are considered as parallel ; they converge to 
a point in the focus of parallel rays in concave reflectors. Even 
in so small and imperfect a reflector as a watch-glass, the focal 
point may, from the concentrated rays of the sun, become heated 
to such a degree as to inflame combustibles. Thus, watch-glass. 
es are sometimes used to light tobacco pipes and kindle fires. — 
The word focus originally signified the burning point, or fire-place. 
The greater the concave surface and the more perfect the reflec- 
tor, the more powerful will be its effect in concentrating the solar 
rays. Metallic concave mirrors have been manufactured of four 
or five feet in diameter ; they are called burning -mirrors. The 
heat at the focus of such mirrors is sufficiently powerful to fuse 
metals, and even earths. The philosopher Archimedes, is said 
to have set fire to the Roman fleet under Marcellus, by means of 
a huge burning mirror. To do this he must have placed the 
mirror in such a position that the concentrated solar rays were 
reflected directly upon the ships of the enemy. 

544. It has been shown that when the incident rays are paral- 
lel, the reflected rays converge to a focus. On the contrary, 
when the incident rays proceed from a focus, or are divergent, 
they are reflected parallel ; thus let a burning taper be placed in 
the focus of a concave mirror ; the ray which falls in the direction 
of the axis of the mirror, is reflected back in the same line, but 

the rays which fall at B and F 
Fig. 200. are reflected to A and E, the dot- 

ted lines being the perpendiculars 
which separate the lines of inci- 
dence and reflection, and show 
their angles to be equal. Or, in 
other words, the diverging rays, 
B and F, are reflected parallel. 
This dispersing of divergent rays, 
is the reverse of collecting par- 
allel rays into a focus, as is done 
* Olmsted. by means of burning-glasses. 

543. Heat produced by concentrating solar rays in small reflectors. Mean- 
ing of the word focus. Burning-mirrors. 

544. Dispersion of rays proceeding from a focus. 




-04 



NATURAL PHILOSOPHY. 



545. It is only when an object is nearer to a concave mirror than its center 
of concavity, that its image is magnified'; for when the object is farther from 
the mirror, the image will appear less than the object, and in an inverted posi- 
tion. Suppose a person, A, stand before a concave mirror below its axis a c, 



Fig. 201. 




and beyond its center of concavity c. A ray of light b a, proceeding from the 
feet would fall upon the mirror at a, and be reflected to i, on the opposite side, 
at an equal angle from the axis a c. The rays b e and b d, also proceeding 
from the feet, are reflected in the lines e i and, d i, and an image of the feet 
appears at i. The rays from the head of the person diverging in like manner 
in all directions, proceed to the points e and d, from whence they are reflected 
in the dotted lines to m, where appears an image of the head. Rays proceed- 
ing from other parts of the body, will also be reflected in their proper positions 
between m and i, where an inverted and diminished image of the whole figure 
appears. This image is beyond the focus / of parallel rays, because of the di- 
verging of the incident rays, and the greater this diverging the more distant 
will be the image from that focus. " Thus if a man place himself directly be- 
fore a large concave mirror, but farther from it than its center of concavity, he 
will see an inverted image of himself in the air between him and the mirror, of 
a less size than himself, and if he hold out his hand towards the mirror, the 
hand of the image will come out towards his hand, and coincide with it, of an 
equal bulk when his hand is in the center of concavity, and he will imagine he 
may shake hands with his image. If he reach his hand further, the hand of 
the image will pass by his hand, and come between it and his body ; and if he 
move his haiid towards either side, the hand of the image will move towards 
the other, so that whatever way the object moves, the image will move the 
contrary way. This appearance of the image in the air between the mirror and 
the object, has been productive of many deceptions, which when exhibited with 
art, and an air of mystery, have been a source of gain to public show-men. 
The images of objects have been exhibited in this manner so as to surprise the 
ignorant, and please the scientific."* 

546. When we consider the various appearances produced by 
the reflection of light from plane, convex and concave mirrors, we 
need not be surprised that advantage has been taken of these na- 
tural phenomena by artful men to impose on the credulous. " The 

* Imison's Elements. 



545, Explain Fig. 201. 

546. Impositions practised by means of optical phenomena, 
ligion and philosophy. 



Union of re* 



RIMRAlTfON OI' LIGHT. 



205 



concave mirror" says Brewster, " is the staple instrument of the 
magician's cabinet, and must always perform a principal part in 
all optical deceptions. It can scarcely be doubted, that a concave 
mirror was the principal instrument by which the heathen gods 
were made to appear in the ancient temples. In the temple of 
Hercules at Tyre, Pliny mentions that there was a seat made of 
consecrated stone, ' from which the gods easily rose.' In order 
to heighten the illusion, intended to be produced by exhibitions of 
objects by reflection from a concave mirror, a great variety of ex- 
pedients are resorted to ; among others is that of a concealed 
chafing-dish, from which issue wreaths of smoke from burning 
perfumes, enveloping the figure and thus causing it to appear as if 
suspended in the clouds. 

We can not too much rejoice in the emancipation of the human 
mind from such bondage, or too much praise the efforts now made 
by men of science, the true priests of nature, to diffuse the knowl- 
edge of her laws, and unveil her mysteries. Religion, too, re- 
leased from the embrace of superstition and deceit, which would 
have strangled her in their grasp, now goes hand in hand with 
science, calling on man to ' praise God for his wonderful works,' 
and adding to the human soul that vital spark of piety, without 
which, philosophy is but a body without a soul. 



LECTURE XXXIII. 



REFRACTION OF LIGHT. 



547. We have considered the various ways in which light is 
reflected by opaque bodies, plane, convex and concave ; we shall 
now pass to the subject of refraction, in which we are to examine 

the manner in which light 



Fig. 202. 




passes through transpa- 
rent bodies of different den - 
sities. 

A ray of light at E C, 
falling through air perpen- 
dicularly, upon a surface of 
glass or water A B, passes 
on in a straight line through 
the body to F ; but if a ray 
in passing from one me- 
dium into another of differ- 
ent density, fall obliquely 
as D h, it is bent from 
its straight course, which 



547. Light passing through transparent bodies of different densities. 

is 



206 



NATURAL PHILOSOPHY. 



would be in the direction D K,and recedes from it, either towards 
L or O, and this bending is called refraction. 

548. If light pass from a rarer into a denser medium, it is re- 
fracted towards the perpendicular. 

Suppose the ray C B to pass 
Fig. 203. obliquely from air into a denser 

medium, water. The course of 
this ray through the air would be 
in the direction C B D, but as 
soon as it enters the water at B, it. 
is bent towards the perpendicular 
ABE, and moves on towards F 




pJNgag= = ~^ between B D and B E, making a 



less angle with the perpendicular, 
than if it had suffered no refraction. 

549. If light pass from a denser 
into a rarer medium, it is refracted 
farther from the perpendicular. 

Let the upper part of the figure 
represent glass, and the lower part 
a rarer medium, viz., water ; and 
let C B be a ray passing obliquely 
from the glass into water ; on ar- 
riving at B, the surface of the rar- 
er medium, the ray does not pass 
on in a straight line towards F, 
but is bent from the perpendicular 



Fig. 204. 




B E, in the line B D, making a 
greater angle with the perpendicu- 
lar than if it had suffered no refrac- 
tion. 
Let A B represent the surface 
which separates the two mediums, 
that from which the ray comes, and 
that into which it enters, this is call- 
ed the refracting surface. The 
ray PC which falls upon it is called 
the incident ray, and the ray C R or 
C S is called the broken or refracted 
ray ; and this, as we have shown, 
varies from the perpendicular E C F 
according as the refracting medium is 
more or less dense. The angle form- 



548. How is light refracted when it passes from a rarer into a denser roe 
dium ? 

549. How refracted in passing from a denser into a rarer medium ? Are 
the angles of incidence and refraction equal ? 



REFRACTIVE POWERS OF BODIES. 



207 



ed by the incident ray P C, with the perpendicular E C, that is, 
the angle P C E, is called the angle of incidence, and the angles 
formed by the refracted ray C R or CS with the perpendicular 
C F, that is the angle F C R or F C S arc called angles of re- 
fraction. On account of the bending which the ray of light un- 
dergoes, the angles of refraction and incidence are never equal.* 

Different Refractive Powers of Bodies. 

550. Transparent bodies differ in their power of bending light ; 
as a general rule, the refractive power is proportioned to the density. 
Thus, the refractive power of water is greater than that of air ; 
the refractive power of glass is greater than that of water, and 
the refractive power of the diamond is greater than all. But the 
chemical constitution of bodies, as well as their density, is found 
to affect their refracting power. Newton first discovered that in- 
flammable bodies possess this power in a high degree, and he 
even ventured to predict that water and diamond might have, in 
their composition, inflammable matter. This hypothesis, which 
appeared so visionary, at that day, has been proved by chemistry 
in the most satisfactory manner. Hydrogen, one of the constitu- 
ents of water, is now known as one of the most combustible of all 
substances ; and diamond, which is crystalized carbon, may be 
burned like charcoal. 

Suppose a ray of light, A P, to 
pass from air into water. Instead 
of proceeding in a straight line to o, 
as it would if not refracted, it will 
be bent in the line P D. If, instead 
of water, the refracting medium be 
sulphur, a denser and more inflam- 
mable substance, the ray will be bent 
in the line P F. If the medium be 
diamond, the refraction will be in the 
line P H. The angle at which wa- 
ter refracts light, or the angle o P M, 
will be seen to be the greatest of all 
the angles of refraction, and the 
angle at which it is refracted by the 
diamond, or the angle H P M, is the 
smallest. 

The angle of incidence, or the 
angle A P L, is the same in the dif- 
ferent cases of refraction. 



Fig. 206. 




Water 
TSul/Jter 
"Hcamond 



* Euler. 



* This is proved by a reference to geometry ; thus, producing the line P C 
to Q, (see Fig. 205,) the angles Q C F and P C E being vertical, are equal to 

550. Bodies differ in their refractive powers. The refractive powers of 
bodies affected by their chemical constitution. Combustible substances 
proved to possess most refractive power. Explain Fig. 206. The sines of 
the angles of incidence and refraction in the same ratio. Total reflection. 



A/ 


D 








R l c 


„„.^S^/e 




"^.y 



208 NATUEAL PHILOSOPHY. 

• 
Let a line A B, be drawn at the shortest distance of the point A from the 
perpendicular L P, this is the sine of the angle of incidence. In the same 
manner is found the sine D C of the angle of refraction of water ; the sine E F 
of the refraction of sulphur, and the sine G H of the refraction of diamond. 

It has been ascertained from many observations, that the sines of the angles 
of incidence and refraction are always in the same ratio ; thus, from air into 
water, the sine of the angle of incidence is to the sine of the angle of refraction 
nearly as 4 to 3, whatever be the position of the ray with respect to the refract- 
ing surface. From air into sulphur, the sine of the angle of incidence is to the 
sine of the angle of refraction as 2 to 1 ; from air into diamond as 1 to -§-. 

Let A C be the ray incident upon the rarer 
Fixr 207 medium R S. It will be refracted from the per- 

°* ' pendicular D F into the direction C E, so that 

the sine A D is to E F in a constant ratio. 

A ray of light cannot be refracted, whenever 
the sine of the angle of refraction becomes equal 
to the radius of a circle. Thus, if we increase 
the angle A C D, the angle F C E will be also 
increased, till the lines C E and F E coincide 
with, or fall upon the radius C S. But if beyond 
this position of the ray A C, the angle A C D is 
still farther increased, it is manifest that its sine 
also is increased ; and consequently, in order 
that the ratio between the sines may be con- 
stant, the sine of refraction E F, must also be 
increased, which is impossible, since we have already supposed it equal to 
the radius C S. 

Thus light falling very obliquely upon a transparent medium ceas- 
es lobe refracted ; but the incident rays are all reflected. This 
is called total reflection. Since the brightness of the reflected 
image depends upon the quantity of light and in ordinary cases of 
reflection a portion of light is absorbed by the reflecting substance, 
those images which arise from total reflection are by far the most 
vivid. 

Familiar Examples of Refraction. 

551. 1st. An oar with one end in water appears bent, and also 
somewhat shorter than it really is. The rays of light from the 

each other, according to the 15th problem of Euclid's 1st Book. The angle 
Q C F then, is equal to the angle of incidence P C E ; therefore the angle of 
refraction R C F or S C F is greater, or less. There are then only two cases 
which can exist ; the one in which the refracted ray being C R, the angle of re- 
fraction R C F is less than the angle of incidence P C E ; and the other, in 
which the refracted ray being C S, the angle of refraction S F C is greater 
than the angle of incidence P C E. In the former case, we say that the ray 
C R approaches the perpendicular, C F ; and in the other, that the refracted 
ray, C S recedes or deviates from the perpendicular. 

551. Why does an oar appear bent in water? Why does a river, under 
certain circumstances, appear more shallow than it is ? Different appear- 
ances of the bottom of a river when viewed perpendicularly and obliquely. 
Example of an object at the bottom of a cup, seen through water. Gold-fish 
in a glass globe. 



KtiFKACTIOX OF THE ATMOSPHERE, 



209 



the eye of the spectator. 
Fig. 208. 




immersed part of the oar proceeding from a denser to a rarer me- 
dium, are refracted from the perpendicular, and inclined towards 
Let o m a represent an oar, the part 
m o being in the air, and m a in the 
water ; the rays diverging from a, 
will appear to diverge from b, nearer 
to the surface of the water ; every 
point in m a will seem nearer to 
the surface than it is in reality, and 
the part of the oar at m a will ap- 
pear to make an angle with the 
part m o. 
2d. The bottom of a river when viewed obliquely appears 
nearer to the eye than it actually is ; for this reason the water 
does not seem as deep as it is in reality. Persons in bathing are 
sometimes thus deceived, and lose their lives in consequence of 
venturing in water beyond their depth. 

3d. When we look from a boat perpendicularly into the water 
of a river, we see the bottom in its true place, because there is no 
refraction. But the more obliquely we view an object seen through 
a transparent medium, the more its position seems changed. 

4th. Take a cup which has the picture of a flower (or other 
figure) at the bottom, and hold it in such a position that the object 
is not visible to the eye at A, being just concealed by the top of 

the cup ; without changing the posi- 
tion of the eye or the cup, let the lat- 
ter be filled with water and the flower 
will now be seen as if at B, although 
the real object is at C. 

5th A gold-fish in a glass globe 
filled with water, sometimes appears 
as two fishes, being seen both by- 
light bent through the surface of the 
water, and by straight or perpendicu- 
lar rays passing through the sides of the glass. In order to see 
bodies under water in their true places and in their true positions, 
the eye should view them through a tube, the farther end being 
closed by a plate of glass, and held in the water. 

552. The atmosphere is a transparent body, becoming more 
dense in proportion as it is nearer the surface of the earth. The 
different strata of air, having different degrees of density, vary 
in their refractive powers. In considering the subject of Acous- 
tics we found the atmosphere to be the great conducting medium 



Fig. 209. 




552. Different refractive powers of atmospheric strata, 
the atmosphere affects light. 

18* 



In what respects 



210 



NATURAL PHILOSOPHY. 



by which sound is propagated. This medium has a no less im- 
portant effect on light, in its transmission, refraction, and decom- 
position. 

553. The heavenly bodies appear higher than they really are r 
because the rays of light, instead of moving through the atmos- 
phere in straight lines, are continually bent towards the earth in 
consequence of meeting with different mediums which become 
denser as they are nearer to the earth. It is supposed that be- 
yond the atmosphere which surrounds our globe, there is, if not a 
vacuum, an atmosphere of a highly rarefied nature, called ether. 
It is proved that the refractive power of the atmosphere is greatest 
at the earth's surface, and diminishes upwards. 

554. The figure represents the difference in the real and ap- 
parent situation of the star A. Rays of light falling thus ob- 
liquely on the earth, would be refract- 
ed in a curve, as in the line A B, and 
seen in the direction of a tangent to 
that part of the curve which meets 
the eye, B C. Thus, the apparent 
altitude is C B. This distance be- 
tween A and C is called the parallax, 
and is of great importance in astro- 
nomical calculation. 

It is owing to their parallax that 
the moon and stars appear above the horizon before they have ac- 
tually risen, and are seen after they have set. The day is length- 
ed from this cause ; for while the sun is yet below the eastern ho- 
rison, he is visible by means of his refracted rays, and his light 
lingers some moments after he has sunk beneath the western 
horizon. 



Fig. 210. 




Fig. 211. 




uation of the sun would 



555. Suppose F 
B to represent the 
earth's surface, and 
G D A the atmos- 
phere. The sun at 
S would appear to a 
spectator at O as if 
situated at C. The 
distance between the 
real and apparent sit- 
lessen until the sun would be in the ze- 



553. Why the heavenly bodies appear higher than they really are. 

554. Real and apparent situation of a star. Parallax. Effects of the par- 
allax of the celestial bodies. « 

555. Explain the effect of the atmosphere upon the sun 1 s rays. 



AERIAL IMAGES. 211 

nith, or directly over the observer, when, as the rays fall perpen- 
dicularly, there would he no refraction. The stratum of air which 
the sun's rays must penetrate, in the horizon, is so much thicker 
and denser than in the zenith, that the light is diminished more 
than 1800 times in passing through it. It is this that renders the 
rays of the sun, at his rising and setting, so much less dazzling to 
the eye than when he is vertical. 

556. " The loss of light, and consequently of heat, by the absorb- 
ing power of the atmosphere, increases with the obliquity of inci- 
dence. Of ten thousand rays falling on its surface, 8123 arrive at 
a given point of the earth, if they fall perpendicularly ; 7024 arrive 
if the angle of direction be fifty degrees; 2831, if it be seven de- 
grees ; and only five rays will arrive through a horizontal stratum. 
Since so great a quantity of light is lost in passing through the 
atmosphere, many celestial objects may be altogether invisible 
from a plain, which may be seen from elevated situations. Di- 
minished splendor, and the false estimate we make of distance, 
from the number of intervening objects, lead us to suppose the sun 
and moon to be much larger when in the horizon than at any other 
altitude, though their apparent diameters are then somewhat less. 
Instead of a sudden transition from light to darkness, the reflective 
power of the air adorns nature with the rosy and golden hues of 
the aurora and twilight. Even when the sun is eighteen degrees 
below the horizon, a sufficient portion of light remains to show that, 
at the height of thirty miles, it is still dense enough to reflect light. 
The atmosphere scatters the sun's rays, and gives all the beauti- 
ful tints and cheerfulness of day. It transmits the blue light in the 
greatest abundance ; as we ascend higher, the sky assumes a 
deeper hue, but in the expanse of space, the sun and stars must 
appear like brilliant specks in the profound blackness."* 

Singular Appearances caused by unusual Refraction, or by Total 
Refection, 

557. To unusual or extraordinary refraction, are referred cer- 
tain phenomena, caused by the unequal density of different portions 
of the atmosphere. We have shown that the incident ray, by fall- 
ing very obliquely, causes total reflection, instead of refraction, p 
Both these causes may be concerned in the production of certain 
appearances, which in a less philosophical age were regarded as 
the effect of magic. The elevation of coasts, ships, and moun- 

* Mrs. Somerville's " Connection of the Physical Sciences." 

556. What effect has obliquity of incidence upon polar light and heat? 
Why do the sun and moon appear largest at the horizon ? Probable appear- 
ance of the sun and stars beyond the earth's atmosphere. 

557. Looming, mirage, &c. 



212 



NATURAL PHILOSOPHY. 



Fig. 212. 



tains, above their usual level, when seen in the distant horizon, is 
called looming. The French have given to the same class of phe- 
nomena, the name of mirage ; and the Italians, who are not unac- 
customed to them in the Straits of Messina, call them the Fata 
Morgana. 

When the rising sun, says an Italian writer, throws his rays at 
an angle of 45° on the sea of Reggio, and the water in the bay is 
calm and unruffled, a spectator on an eminence above the city, 
who places his back to the sun and his face to the sea, sees, as if 
upon the surface of the water, castles, arches, columns and towers, 
palaces and churches, with balconies and domes ; vallies and 
plains covered with herds and flocks ; men walking and riding, 
and a variety of strange and grotesque figures, rapidly succeeding 
each other. When the atmosphere is charged with vapors and 
exhalations to the height of about twenty feet, the same objects, 
with less distinctness of outline will appear in the mists and vapors 
floating in the atmosphere, as if suspended there. This aerial re- 
presentation of the objects on the opposite coast, as first described 
in 1793 was scarcely credited, until subsequent statements showed 
that others had observed similar appearances in other places. 

558. In 1798, at Ramsgate, England, a ship was ob- 
served, which appeared as at A, the top-mast being the 
only part which was seen above the horizon. An in- 
verted image was seen at B just above the real ship A, 
and finally an erect image at C. The sea was seen as 
at V W. As the ship A rose to the horizon,* the image 
C gradually disappeared, and the image B descended 
towards A. After the whole ship was above the hori- 
zon, the two images B and C were distinctly seen. 

An English captain at sea, knew a ship by its invert- 
ed image in the air, when the ship itself was below the 
horizon, or entirely out of sight. " It was," said he, 
" so well defined that I could distinguish by a tele- 
scope, every sail, the general rig of the ship, and its par- 
ticular character, so that I confidently pronounced it 
my father's ship, the Fame, which it afterwards proved 
/ / iJMJ. to be, though in comparing notes with my father, I 

jtf found that he was about 30 miles distant, and seven- 

■"^•rr teen miles beyond the horizon." 

559. " Let S F be a ship in the horizon, and visible 
to the eye at E, by rays S E, F E proceeding in a 
straight line to E, through a tract of the atmosphere in 
its usual state. If we suppose that the refractive power 
of the atmosphere above the line S a E varies, so as to 
be less at c than at a, then rays S d, F c proceeding up- 
wards from the ship, and which could not in the ordi- 

* The pupil will recollect that owing to the rotundity of the earth, the 
top of an approaching ship at sea is the part first seen. 

558. The ship Fame known by its aerial image. 

559. Aerial representation of a 6hip. 





MIRAGE. 



213 



nary state of the air, reach the eye at E, will be refracted into curve lines F c, 
S d ; and if the variation of refractive power is such, that these last rays crosa 
each other at x, then the ray S d, in place of being the uppermost, will now be 
the undermost, and, consequently, will enter the eye as if it came from F. 

If we now draw lines E s, E P, tangents to these curve lines at E, these lines 
will be the direction in which the ship will be seen by the rays F c, S d, and the 
observer at E will see an inverted image P s of the ship S F considerably ele- 
vated abovo the horizon. The refractive power of the air still continuing to di- 

Fig. 213. 




minish, other rays, S n, F m, that never could reach the eye at E in the ordi- 
nary state of the atmosphere, may likewise be bent into curves which will not 
cross each other before they reach the eye at E. In this case, the tangent E I, 
to the upper curve S n E, will be uppermost, and the tangent E D, to the lower 
curve FmE, lowermost, so that the observer at E will see the erect image D I, 
of the ship above the inverted image. It is possible that a third, and even a 
fourth image may be seen by similar refractions."* 

560. The mirage is common in hot climates on sandy plains. 
In the middle of the day when the sun shines on the level sur- 
face of the sand, the appearance of a sheet of water is observed 
at a little distance ; and so complete is the deception, that any per- 
son ignorant of the cause, would not doubt but he was approaching 
a lake or river. This spectral body of water reflects the animals, 
trees or mountains around, with great distinctness. As the trav- 
eler, perhaps fainting with thirst, advances, the tantalizing phan- 
tom of water recedes, exhibiting on its surface new images of 
surrounding objects. A traveler in India thus describes a phe- 
nomenon of this kind. " A deep precipitous valley below us, at 
the bottom of which I had seen one or two miserable villages in 
the morning, bore, in the evening, a complete resemblance to a 
beautiful lake ; the vapor which played the part of water, ascend- 

* Treatise on Optics — Library of Useful Knowledge. 

560. Deceptive appearances by means of the mirage. Mirage described 
by a traveler in India. Supposed cause of the mirage. Appearance wit- 
nessed by Dr. Buchan at Brighton. 



214 



NATURAL PHILOSOPHY. 



ing nearly half way up the sides of the vale, and on its bright 
surface trees and rocks were distinctly reflected." 

Some writers attribute the mirage chiefly to partial, or total re- 
flection of the rays of light at the surfaces of atmospheric strata 
of different densities. The following occurrence which happened 
in November, 1894, is supposed to have been produced by a simi- 
lar cause. " Dr. Buchan, while watching the rising sun from 
the cliff about a mile to the east of Brighton, England, at the in- 
stant the sun emerged from the surface of the ocean, saw the cliff 
on which he was standing, a wind-mill, his own figure, and that of a 
friend, depicted immediately opposite to him, on the sea. This 
appearance lasted about ten minutes, till the sun had risen nearly 
his own diameter above the surface of the waves. The whole 
then seemed to be elevated into the air and successively vanished. 
The rays of the sun fell upon the cliff at an incidence of 73° from 
the perpendicular, and the sea was covered with a dense fog many 
yards in height, which gradually receded from the rising sun." 

561. Dr. Wollaston has proved, by simple experiments, that the appear- 
ance of double images is owing to the refraction of rays through mediums 
of different densities. 

Experiment. If you pour some spirits of wine or alcohol in a bottle con- 
taining water, the spirits of wine, unless the water is agitated, will remain 
in a distinct stratum at the top ; on looking at any object behind the bottle, 
or through these mixed strata, an inverted image of the object will appear. 
Syrup is more dense than water, therefore the same ef- 
fect will be produced by looking at an object through 
strata of syrup and water. Dr. Wollaston poured into 
a square phial a small quantity of clear syrup, and above 
this he poured an equal quantity of water, which grad- 
ually combined with the syrup, as seen at A. The 
word Syrup upon a card held behind the bottle, ap- 
peared erect when seen through the pure syrup, but 
inverted, as represented in the figure, when seen 
through the mixture of water and syrup. Dr. Wollas- 
ton then put nearly the same quantity of rectified spirit 
of wine above the water, as in the figure at B, and he 
saw the appearance there represented, the true place 
of the word Spirit, and the inverted and erect images 
below. By looking along a red hot poker at a distant 
object, an erect and an inverted image is seen. This 
is in consequence of the change produced in the den- 
sity of the air produced by the heat. The air nearest the heated poker be- 
ing most rare, its refractive power is least. 

562. " We have no doubt, ' says an English writer, " that some of the facts 
ascribed in the Western Highlands of Scotland to second sight, have been 
owing to the unusual refraction of the atmosphere, and that the same cause 
will explain some of those wonders which sceptics discredit, and which su- 
perstitious minds attribute to supernatural causes. The beacon-keeper of the 

561. Experiments by Dr. Wollaston with refracting mediums of different 
densities, 

562. Strange appearances accounted for by unequal refraction. 






Fig. 214. 




LENSES. 215 

Isle of France, who saw ships in the air before they rose above the visible 
horizon, may now recover his good character in the eyes of the former, while 
the latter may cease to regard him as a magician." Our country has its su- 
perstitious legends of wonderful sights, attested by veritable witnesses. The 
Phantom Ship of the Puritans, and the Flying Dutchman of the settlers of 
New Amsterdam, were probably real apparitions, for we find that unequal 
refraction may cause a ship to appear as if suspended in the clouds, or pro- 
duce the phantom of a ship, while the real object is out of sight. 



LECTURE XXXJV. 

LENSES. 

563. Glass, in various forms, is the substance most used for re- 
fracting the rays of light in optical experiments, and for optical 
instruments. 

1st. An optical prism, A, is a solid, having two plane surfaces 
A R, A S, inclined to one another, these are called its refracting 
surfaces. 2d. A plane glass, B, has two plane surfaces parallel to 
one another. 3d. A sphere or spherical lens, C, has every point 
in its surface equally distant from a common center, O. 

4th. A double convex lens, D, is 

Fig. 215. bounded by two convex spherical 

surfaces, whose centers are on oppo- 

ABC DEFGHI site sides of the lens. When the 

radii of its two surfaces are equal, it 

N is said to be equally convex ; when 

the radii are unequal, it is said to be 

R s unequally convex. 

5th. A plano-convex lens, E, is bounded by a plane surface on one 
side, and a convex one on the other. 6th. A double concave lens, 
F, is bounded by concave surfaces on both sides. 7th. A plano- 
concave lens, G, is bounded by a plane surface on one side, and a 
concave on the other. 8th. A meniscus, H, is bounded by a con- 
cave and a convex spherical surface ; and these two surfaces meet 
if continued. 9th. A concavo-convex lens, I, is bounded by a 
concave and a convex surface ; but these two surfaces do not meet 
though continued. 

The axis of these lens is a straight line, M N, in which are 
situated the centers of their spherical surfaces, and to which their 
plane surfaces are perpendicular. 

563. What substance is most used in optical experiments ? Prism. Lenses 
Axis of the lenses. 



M© 



216 



NATURAL PHILOSOPHY. 




564. The most simple case of 
refraction is, when the refracting 
substance is terminated by plane 
surfaces, parallel to each other. — 
Suppose M N to be a piece of 
glass, terminated by plane sur- 
faces, and that the ray A C falls 
obliquely at the point C. On en- 
tering the glass, the direction of 
the ray will be bent out of the 
straight line C D, and will move 
towards the perpendicular O P, 
through the glass, in the line C e. On leaving the glass, the ray is 
again refracted, but in a contrary direction ; or from the perpen- 
dicular O P towards D. A ray, therefore, passing obliquely 
through a transparent body of parallel surfaces, has its course 
turned from the original direction, but, after refraction, proceeds 
in a line parallel with that direction ; thus, E e is parallel with b 
D. This refraction takes place in the light which passes through 
glass windows ; but owing to the thinness of the panes, the appa- 
rent varies little from the true situation of the objects thus seen. 
When the two surfaces of a pane of window glass are not planes, 
or are not perfectly parallel to each other, objects seen through 
the glass appear more or less distorted. 

565. A lens* is usually of glass, ground into such a form as to 
collect or disperse the rays of light which pass through it. 

A convex lens collects, and a concave lens disperses rays of light. 
The sphere of a lens is an imagin- 
ary circle, of which its surface is a 
portion. The circle A B C is the sphere 
of the convex lens D. 

The radius of a lens is the radius 
of its sphere, D E; and a line D <f 
passing through its center, is its axis. 
566. The focus is a point be. 
yond the convex lens where the re- 
fracted rays meet. This point depends 
upon the form of the lens, and the re- 
fracting power of the substance of 

* From the Latin, lentil, a bean. It was the double convex, to which 
the name lens was first applied. This has its two sides convex, like a bean. 

564. Cause of refraction when the refracting surface is terminated by 
plane, parallel surfaces. Refraction of glass windows. 

565. Definition of a lens. Effects of a convex and concave lens upon 
light. The sphere of a lens. Radius of a lens. 

566. Focus of a convex lens. What renders the focus more distant ? 



Fi£. 217. 




CONVEX LENSES. 



217 



which it is composed. The less convex or bulging the lens is, 
the more nearly it approaches a plane glass, and consequently the 
more distant is its focus. The more convex or bulging a lens is, 
the more obliquely will the rays, at any distance from the center, 

Fig. 218. 




Fig. 219. 



fall upon the surface ; and the sooner, in consequence of their being 
more bent, will they meet the axis. Thus a, which is a sphere, 
would converge the rays sooner than d, and the latter would con- 
verge them sooner than the less convex lens c. 

Convex Lenses. 

567. Let A B be a convex glass, exposed to a distant object E 
F, whose rays G A, Gc, G B fall on the glass, and passing 
through it, undergo a refraction, which will take place in such a 
manner, that the rays proceeding from the point G shall meet on 
the other side of the glass, in the point g. The same thing will 
happen to the rays which proceed from every point of the object. 
The refracted rays A Z, B m, C c, will pursue the 
same direction as if the object were at e f, and in- 
verted ; and the object will appear as many times 
smaller as the distance c g shall be contained in the 
distance c G. Such a glass represents the object, 
E F, behind it, at e f ; this representation is called 
the image, which is consequently inverted, and is 
smaller than the object, in proportion as c g is less 
than c G. 

If the sun were the object, the image represented 
at e f would be the image of the sun ; though 
very small, it would be so brilliant as to dazzle the 
eye, for all the rays which pass through the glass 
meet in this image, and therefore exercise an in- 
creased power of giving light and heat. Combustible 
substances placed in the focus of such a glass are in- 
stantly consumed. Metals are melted, and even vitri- 
fied by it ; and other effects are produced far beyond the 
reach of the most active and intense fire. The reason for these 

567. How does an object appear when viewed through a convex lens? 
Why would the sun's rays at c f, Fig. 219, be very intense? How does a 
convex lens differ from burning-mirrors 1 

19 




215 



yATUKAI, PHILOSOPHY. 



Fig. 220. 



effects is the same as in the case of the burm^g-inirrror. In both 
cases the rays of the sun diffused over the whole surface of the 
glass, are collected in the small space of the sun's image. The 
only difference is. that in the mirror the rays are collected by re- 
flection, and in the convex glass by retraction. 

568. Second illustration of tie appearance of objects re- 
presented by a convex lens. 

Le: A B C D be a co;. before which is placed 

an object E G F. The ray from the point E, fall 

npon the g : atained in the space A E B ; and are 

aU collected in the space A e B by refraction, so as to meet 
in the point e. In the same manner, the rays from the 
point G. which fall on the glass, and which fill the space 
A G B. are comprehended by means of refraction in the 
space A g B. and meet in the point g. Finally the rays 
from the point F. which fall on the glass in the angle A F B, 
are refracted so as to meet in the point/. Thus we shall 
have the image e gfin an inverted position behind the 
r.iss : and as many times. smaller than the object, as the 
distance D ? is smaller than the distance C G. 

In order to determine the place of the image e g f, \ 
we must attend as well to the form of the glass, 
as to the distance of the object. As to the first, 
it may be remarked, that the more convex the 
glass is. or in other words, the more the thick- 
ness of the □ D. esceeeds that of the ex- 
tremities, the nearer the image will be to its surface. With 
regard to the distance, if we bring the object E F nearer 
to the glass, its image e t retires from it. When the object, 
then, is very distant, the image falls in the very focus ; and 
the nearer we bring the object to the glass, the farther the 
image retires from it, and that in conformity to a law in op- 
by means of which we can always determine the place of 
the image for every distance of the object, provided we know the 
focus of the glass. The point where the rays meet is. as has 
been said, the place of the image. This point is easily found by 
experience. The different denominations of optical glasses are 
derived from it. as when we say. such a glass has its focus at the 
distance of an inch, another at the distance of a foot, another at 
the distance of ten feet, and so on : or more concisely, a dass of 
an inch, a foot, or ten feet focus. 

569. To prove that a concave lens disperses ravs of light, let 
A and C be rays falling upon the concave lens D E : instead of 
converging from a and c towards b in the axis of the lens, 







568. How is the subject of vision through convex lenses farther illustrated ? 
What is meant by a glass of one inch or one foot focus ? 

569. Effect of a cuucave lens. How are convex and concave lenses used 



219 



they will, diverge to d and e. A 
perpendicular ray B b passes on in a 
straight line without any refraction. 
It will be seen that, as the rays A C 
diverge on leaving the glass, they can- 
not, without another refraction, ever 
be brought to a focus. A convex lens 
by collecting these diverging rays can 
bring them to a focus. 

Concave lenses are, in like manner, 
used to receive converging pencils of 
rays, and to restore them to their ori- 
ginal direction ; thus these different lenses, in combination, are ap- 
plied to most important uses, in the construction of optical instru- 
ments. 

570. Of the images formed by concave lenses. 

Let A B C be a concave lens. If the object E G 
F, be exposed to it, the rays G A, G C, G B, pro- 




Fig. 222. 



ceeding from the point G, will undergo a refraction, 
on leaving the glass, in the direction of A Z, C m, and 
B ra, as if they had issued from the point g ; and an 
eye placed behind the glass, at m, for example, will 
see the object just as if it were placed at e g f, and in 
a situation similar to that in which it is at the point G, 
but as many times smaller as the distance C G ex- 
ceeds the distance G g. Convex glasses represent the 
image of a very distant object behind them, concave 
glasses represent it before them ; the former represent 
it inverted, and the latter in its real situation ; in 
both, the image is as many times smaller as the dis- 
tance of the object from the glass, exceeds that of 
the glass from the image. On this property of glasses 
depends the utility of telescopes, spectacles, and mi- 
croscopes. 

Vision. 

571. Who can estimate the value of sight, without which, 

" Day, or the sweet approach of ev'n or morn, 
Or sight of vernal bloom, or summer's rose, 
Or flocks, or herds, or human face divine," 

would " ne'er to us return." And even though we might see 
the objects immediately around us, and those above us in our 
own atmosphere, but could not extend our vision beyond these 

570. How are objects represented by a concave lens ? 

571. Advantages of sight 




220 



NATURAL PHILOSOPHY. 



limits, of what sublime enjoyments should we be deprived ! Con- 
fined as the soul is to a portion of matter which cannot soar be- 
yond this terrestrial ball, if all beyond its atmosphere were dark 
and unfathomable, what a gloomy pall would hang over us ! 
But we are permitted to contemplate the system of worlds of 
which ours forms a portion ; and the splendors of God's cre- 
ation are revealed to our wandering gaze. We learn the motions 
and laAvs which govern our own planet, by seeing and observing 
those of others. Our imaginations are awakened by the beauty 
and sublimity of the glorious firmament, and our hearts are 
warmed with love and admiration for Him who created this mag- 
nificent universe. How greatly then are science, poetry and devo- 
tion, indebted to the power of distant vision. 

The Eye. 

572. The eye, by turns a microscope and telescope, is adapted 
to the purpose of viewing things near, or of extending its field of 
vision to far distant objects. On examining the structure of the 
eye, we find it a beautiful optical instrument made in strict con- 
formity to the laws of science, and perfectly fitted to be acted 
upon by light, so as to form an image of the object from which 
light is reflected. Was the Artist who formed this instrument 
ignorant of the effects to be produced ? Or did the instrument 
itself blunder into existence, the offspring of chance or accident? 
We may not pursue these speculations ; but cold must be the 
heart of him, who in studying these subjects, does not see some- 
thing beyond the mere enunciation and illustration of scientific 
truths, and whose devout affections are not animated, as his under- 
standing becomes enlightened ! 

573. The eye when viewed superficially, consists of the white, 
the iris, and pupil, but, by means of anatomical dissection, various 
other parts have been discovered. 

"The figure exhibits & front view 
of the eye ball. The white part 
surrounding the center is called the 
sclerotic* coat a a, and it is continued 
within the orbit, round the back part 
of the eye ball, being formed of a 
dense membrane, which includes, as 
in a bag, the other parts of the eye. 
It is perfectly opaque, and therefore 
is not continued over the front of the 

* From the Greek, sMcros, hard. 



Fig. 223. 




572. The eye an optical instrument. Could not have been the result of 
accident. 



573. Describe the eye as represented at Fig. 223. 



THE EYE. 



221 



eye, but joins the transparent cornea,* b b„ which differs from 
the sclerotic coat, in being completely pervious to light, and there- 
fore serving like a window to admit light to the interior of the 
eve. Included within the cornea is the iris,~\ somewhat resem- 
bling a colored fringe, usually either of a dark brown, or a gray- 
ish blue tint ; and hence the distinction between black, and blue, 
or gray eyes. In the center of the eye, surrounded by the iris, is 
a dark, circular space of variable dimensions, called the pupil, 
through which the rays of light pass into the chambers of the eye. 

574. A horizontal section of the 
eye shows that it is enveloped in 
four membranes or coats ; the scle- 
rotic coat AAA; the cornea B, 
connected with the former, in the 
front of the eye ; the choroid^ coat 
T T, which forms a lining to the 
sclerotic, and, on its opposite sur- 
face, is covered by a black pig- 
ment on which lies the interior coat 
of the eye, called the retina^ R R, 
a delicate net-work expanded over 
the inner chamber of the eye, and 
proceeding from the optic nerve, O, by which sensations are 
supposed to be conveyed to the brain. The interior of the eye, or 
the cavity surrounded by the coats just described, is filled by three 
substances called humors : The first, or the aqueous humor, D, is a 
fluid situated immediately behind the transparent cornea. The 
second, the crystalline humor, C, is directly behind the iris, being 
a solid, transparent lens, more convex behind than before ; the 
third, called the vitreous humor, V, a kind of viscous, solid mass, 
contributing chiefly to preserve the globular figure of the eye. 
Between C and D is the pupil or opening in the iris, I I, through 
which light is admitted into the eye, and behind which the crys- 
talline humor or lens is suspended in a transparent capsule, by the 
ciliary processes, L L, which proceed from the Iris. 

575. We find, therefore, that the eye has/owr coats or membranes, 
viz.; the sclerotic, the cornea, the choroid, and the retina ; two humors, 
viz ; the aqueous and vitreous ; and one lens, viz. ; the crystalline. 

* From the Latin corneus, horny, or like a horn. 

t So called because it has many colors like the rainbow or Iris. 

X From the Greek, Korion. 

§ From the Latin, rete, a net. 




574. What does the interior of the eye present? 

575. How many coats and humors has the eye? Situation of the eyes, 
use of muscles, eye-lids, &c. 

19* 



222 NATURAL PHILOSOPHY. 

The eyes are situated in basin-shaped cavities in the skull, called 
the orbits, and there are various muscles attached to the ball of the 
eye, and to different parts of each orbit, which, by their contrac- 
tion, give a certain degree of lateral rolling motion to the eye, and 
thus assist in directing the sight towards particular objects, at 
pleasure. The eye-lids, also, moved by muscles and fringed by 
eye-lashes, serve to guard the eyes from dust, and to screen, or shut 
them altogether, from the access of too intense a light; and there 
are glands for the secretion of fluid to moisten the cornea, and, by 
the motion of the eye-lids, keep its surface clear, and in a state 
adapted to perfect vision. 



LECTURE XXXV. 

VISUAL ANGLE. FORE-SHORTENING. PERSPECTIVE. INTENSITY 

OF LIGHT AND SHADE. CONVERGENCE OF THE OPTIC AXES. 

576. The great purposes of vision are to distinguish the mag- 
nitude, figure, and distance of objects. The means of effecting 
this are, 1st. by the visual angle, or the angle under which objects 
are seen ; 2d. the intensity of light, shade, and colors ; 3d. the 
divergence of the rays of light, and the convergence of the optic 
axes. 

1. The Visual Angle. 

577. The field of view is that open space around us, in which 
objects are seen. But the eye has not the power of taking in, at 
one view, the whole circle of the horizon. When a person stands 
with his face to the east, he cannot see the western horizon ; nor 
can he, at one view, behold both the north and the south ; be- 
cause the range of human vision is less than half the circumfer- 
ence of the horizon. The scope of vision for the eye of man is 
not far from 45°, or one eighth of a circle. Within this range the 
distant landscape, with its numerous objects, may be depicted upon 
the retina of the eye. That is, a portion of the rays of light which 
diverge from objects in straight lines in all directions, falling upon 
the eye, are refracted by its transparent medium, and form a mini- 
ature picture upon the retina. 

57G. Objects of vision, and means by which they are perceived. 
577. Field of view. Extent of the field of view. 



VISUAL ANGLE. 



223 



Fig. 225. 



578. Suppose a person to be surrounded 
by a globe of glass, divided into equal de- 
grees; he would, then, be able to know, ex- 
actly, what portion of Ids field of view was 
occupied, or intercepted, by any particular 
object, as the cross ate; and he would be 
able to judge of its relative size and situa- 
tion. If the transparent globe were small as 
at a d, or larger as at b f, ore g, the part of its 
surface apparently occupied by any object 
beyond, or within it, would bear a similar 
proportion to the whole surface; thus, the 
cross at a d bears the same proportion to the 
small circle that b f and c g bear to the lar- 
ger circles. Every circle being supposed to 
be divided into 360 degrees, (which degrees 
are, of course, smaller in a small circle, than 
in a larger one,) the magnitudes of objects 
are estimated, by observing how many of 
these degrees of the field of view each one 
occupies. The most convenient way of mea- 
suring a part of a circle of which the whole 
is not seen, is to measure the angle formed 
at its center, by lines drawn from the ex- 
tremities of that part. In the figure, the an- 
gle at e being formed by the lines c e and g e, the object c g is said to oc- 
cupy a certain number of degrees of the circumference of the circle, or to 
subtend an angle of a certain number of degrees at its center, which angle 
is called the vitual angle. The objects at b f and a d subtend the same an- 
gle as the larger, but more distant object at c g. But the cross c g, which 
is about three times as large as a d, is also three times as far from the eye, 
and yet if no idea of their comparative distances entered into the computa- 
tion of their magnitudes, the spectator, judging only from the visual angle, 
would suppose them to be of the same size. 

579. Let A B represent a tree, with pencils of divergent rays 
assuing from the top and bottom. Entering the pupil of the eye, 
C, the rays are refracted by the crystalline lens, D, and form at 




Fig. 226. 




the retina, a b, an inverted picture of the tree. The nearer the 
tree is to the eye, the greater is the angle made by the meeting 
of the lines which proceed from the top and bottom. 

578. What is represented at Fig. 225 ? What is meant by the visual angle ? 

579. Tree seen at a distance. Man viewed at different distances.' 



224 



NATURAL PHILOSOPHY. 




Fig. 227. Again, let A B represent a man 

viewed by an eye at C ; the ex- 
treme rays proceeding from this ob- 
ject form the angle A C B. The 
angle at C is the visual angle. If 
the same object be viewed at the 
point D, the visual angle ADB 
will be greater. An object A B, 
seen at C, appears less than the 
same object seen at D, where the visual angle is greater ; thus a 
tall man at a distance, may appear smaller than a child which is 
near. At four miles distance and without any interposing object, 
a man ceases to be visible. 

580. " Astronomers measure very accurately the angles under 
which we see the heavenly bodies ; and they have found that the 
visual angle of the sun is somewhat more than half a degree. If 
the sun were twice as far from us, this angle would be reduced 
to the half; and then it will not seem surprising that it should 
furnish us four times less light. And if the sun were 400 times 
further off, his visual angle would become so many times less, and 
then that luminary would appear no greater than a star. We 
must therefore carefully distinguish the apparent magnitude of any 
object from its real magnitude. The first is always an angle 
greater or less, according as the object is nearer or more distant. 
Thus the apparent magnitude of the sun is an angle of about half 
a degree, whereas his real magnitude far surpasses that of the 
earth ; for the sun being a globe, his diameter is estimated to be 
about 790,000 English miles, while the diameter of the earth is 
only 7912 English miles."* If we should ask a child or an ig- 
norant, unreflecting person, whether the moon is larger than a 
carriage -wheel, he would probably answer you in the negative. 
One better informed would tell you that the moon's distance when 
seen from the earth, greatly diminished its apparent size ; and he 
would explain this phenomenon by showing that the apparent mag- 
nitude of objects depends upon the greater or less extent of the 
visual angle. 

Vision requires the Aid of Experience, 

581. The real magnitude and distance of objects is not deter- 
mined by vision alone. We learn to judge of things unknown, by 

* Euler. 



580. Visual angle of the sun. Apparent and real magnitude of objects 
Apparent magnitude considered real. 

5.81. Real magnitude not determined by vision alone. Doubts of Philoso- 
phers. Appearance of objects to a person who has suddenly received sight. 
Learning to see. Method by which painters give the effect of distance. 



l'OHK-SIIOUTKMMJ. M2-) 

comparing them with such as arc familiar. When we see a per- 
son whom we know, walking at a distance with a stranger, we 
judge of the height of the latter by comparison. The visual 
angle assists in forming a judgmont as to the distance of an object 
when its real magnitude is known. When the size of a distant 
object is known, its distance may be determined ; so on the other 
hand, when the distance is known, the size may be ascertained with 
sufficient accuracy. 

Philosophers are in doubt as to the extent of knowledge of external things 
gained by sight, whether we are indebted to this sense for our knowledge 
of the figure and magnitude of bodies. An instance is related by the cele- 
brated optician, Chesselden, of his having, by means of a surgical operation, 
givem sight to a man who was born blind.* " This person," it is said, " was 
at first dazzled ; he could distinguish nothing as to the magnitude or distance 
of objects. All objects appeared so near that he wanted to handle them. 
And considerable time and long practice were requisite to bring him to the 
real use of sight. He was under the necessity of serving a long apprentice- 
thip, such as we perform during the term of childhood, and of which we 
afterwards preserve no recollection. This apprenticeship it is, which in- 
structed us, that an object appears to us so much the more clear and distinct 
as it is nearer; and reciprocally, that an object which appears clear and dis- 
tinct is near; and when it appears obscure and indistinct, that it is at a dis- 
tance. It is thus that painters, by weakening the tints of the objects which 
they wish to appear remote, and strengthening those which they would re- 
present as nearer, are enabled to determine our judgment conformably to 
the effect which they mean to produce. And they succetd so perfectly, that 
we consider some of the objects represented in painting as more distant than 
others ; an illusion which could not take place if vision discovered to us the 
real distance, and magnitude of objects. "t 

582. Fore-shortening. The appearance of objects to the eye de- 
pends much on their position. A globe always presents a circular 
image in whatever manner it may be viewed ; but an egg may 
appear circular or oval, according to its position. A wheel when 
viewed in front, appears a perfect circle, when seen edgeways it 
appears like a broad straight band, and in other positions it ap- 
pears oval. The sight of an object suggests the knowledge of its 
actual figure which w r e have gained by previous experience, and 
we think of its true figure rather than of the outline presented to 
the eye. Whoever attempts to draw from nature finds a difficulty 

* The disease which occasioned the blindness referred to, is called a cata- 
ract, (from the Greek, katarasso, to confound or disturb.) It arises from the 
opacity of the crystalline lens, which is thus rendered unfit for its purpose 
of refracting light. By removing the lens out of the axis of vision, sight 
may be restored, if the retina is not diseased. This operation is called 
couching. In some cases the opaque crystalline lens is extracted. Glass 
lenses may be substituted for the lens of the eye for the purpose of collect- 
ing the rays of light. 

t Euler. 

582. Apparent figure of objects depends on position. Effect of experience 
upon our judgment of things »een. Difficulty of drawing from nature. 



226 NATURAL nilLOSOrifY. 

in delineating objects as they appear. In drawing a row of trees 
of equal size, as they would appear to a person standing at one 
extremity, the nearer trees must be represented larger. If a stick 
of timber be placed with one end directly before the eye, and on a 
line parallel with it, that end, only, will be seen ; if one of the sides 
be placed before the eye, the whole length will be seen ; in any 
intermediate position, it will appear more or less shortened ; the 
outline on the retina being similar to the shadow it would presenc 
on the wall, in the direction of the person viewing it. 

583. Painters term the appearance of the surfaces or lines, 
when so placed as to face the spectator, fore-shortening. On 
looking abroad upon the extended surface, the distant portions^re 
fore-shortened in proportion as they recede from the eye. Sup- 
pose a man standing on a plain at c ; 

Fig. 228. on looking down, he sees a portion of 

the surface with very little fore-short- 
ening ; an extent of five feet, as a d, (that 
is, allowing five feet to be the height of 
the eye) will subtend in the eye, an 
angle of 45°, viz. the angle a c d; or 
in other words, it will appear 45° in his 
field of view T , in half of what is subtended by the whole space from 
his feet to the horizon ; the next five feet will subtend the angle 
d cf the next five feet the angle f c g, and the next five feet the 
angle g c b. Thus, as the man carries his view more and more 
forward, lines from the surface come to his eye more and more 
obliquely, until, at last, the light coming from the surface seems 
to be on a level with the eye. By understanding the effect of this 
fore -shortening, we partly judge of the distance and magnitude of 
the objects situated at various points of view. 

Perspective. 

584. The word perspective is from the Latin per, through, and 
specio, to look. The science of perspective teaches to draw on a 
plane surface true pictures of objects, as they appear to the eye, 
from any distance in an oblique position. 

Suppose a straight view of the stone blocks or pillars (Fig. 229) extending 
from a to S, to be viewed by a person standing near C ; then, because objects 
appear smaller to the eye in exact proportion to their increased distance 
from it, the second block, if twice as far as the first, would appear only 



583. Meaning of the term fore-shortening. Effect of extending the view 
over a large surface. 

534. What is perspective? Buildings, trees, and pillars seen in per- 
spective. Vanishing point. 



PERSPECTIVE. 



227 



Fig. 229. 



W 








II 


III 


III 


^W 


^S ^ 


dtf&m 


'{ 


I] 


til 


III 


in 


in hi. .. 








i'£' 


II II 


til 


yi^v^^ 










^ 


— ^a 




G . 


irt 


JJi 



half as large ; the third, if three times 
as far, would appear only one third as 
large, and so on to any extent, and for 
any other proportions; and if the l,000lh, 
or any other nearer or more distant 
pillar, subtended to the eye an angle 
less than the sixtieth of a degree of the 
field of view, it would be altogether 
invisible, even if nothing intervened 
between it and the eye. Where the 
row ceases to be visible from the mi- 
nuteness of the parts, or from the fact 
of the nearer objects concealing the 
more remote, it Tnay be said to have 
reached its vanishing point. 
585. It is very remarkable that in any such case of a straight line, or row 
of trees or pillars vanishing from sight, in whatever direction it points, east 
for instance, although the eye to see the near end of it would have to look 
about north-east, still the point in the heavens, or in a picture, or transparent 
plane before the eye, where the line would vanish, would be exactly east 
from the eye, and not in the slightest degree either to the north or to the 
south of the east point, because the pillars happened to be north or south 
of the individual ; and therefore, if there were two or more rows of pillars 
parallel to the first, but considerably apart from each other, as the lines 
a S, b S, d S, c S, and/S, still all would vanish, or seem to terminate in 
the very same point of the field of view. The reason of this is easily un- 
derstood. Let us suppose a line drawn directly east from the eye, or to the 
point S, viz. a line directly over the line b S, and that the line of pillars a S, 
also pointing east, is 20 feet north of the spectator, and the line b S, running 
in the same direction, is 20 fe t south of him, then, evidently, for the same 
reason as the space between the top and bottom of the pillars, that is to say 
their height, becomes apparently less as their distance from the eye in- 
creases, so will the space between each pillar and the point corresponding 
to its place in the visual ray, or line along which the eye looks, become less, 
and the lines of pillars really 20 feet apart from the visual ray, will, at a cer- 
tain distance from the eye, viz. where 20 feet is apparently reduced to a 
point, appear to join it, and the three lines will appear to meet in that point, 
beyond which they cannot be visible, and which is therefore called the van- 
ishing point. 

586. The conception of this truth may be facilitated by our supposing a 
star or planet to be rising in the eastern point of the heavens, at the moment 
of observation ; then, if the three parallel lines were continued on to the 
planet, and were visible as far, they would arrive there with the 20 feet of 
interval between them just as they left the earth ; but as any planet, although 
many thousand miles in diameter, owing to its distance from the earth, ap- 
pears only a point, much more would the space between any two lines only 
20 feet apart be there undistinguishable by human sight. And what is true 
of a space of 20 feet between parallel lines, is equally true, as regards human 
vision, of a space of hundreds of thousands of miles ; as a general rule, there- 
fore, it holds, that all lines parallel to each other in perspective lend to and fin- 
ish in the same vanishing point, viz., the situation of the line in which the 
eye looks when directed parallel to any one of those real lines. And this is 
true not only of lines of the same level or horizontal plane, viz., such as 

585. Explanation of the vanishing point in a picture. 

535. Suppose three parallel lines twenty feet apart to be continued to a 
planet or star. General rule in perspective with regard to parallel lines. 



228 



NATURAL PHILOSOPHY. 



might be along the surface of the sea, but also of lines that are vertical or 
one above another, as those running along the tops and bottoms of the pil- 
lars, (Fig. 229,) or along the roofs and windows of the houses, and in- 
deed of all lines in whatever situations, provided they are parallel to the 
visual ray. 

587. When it is ascertained, therefore, that a line in any natural or artifi- 
cial object, points 10 or 20 or any number of degrees north or south, or above 
or below the center of the scene or picture, that is to say, the point of 
sight, or principal visual ray, then also is it known that all the parallels to 
that line have their vanishing point in that spot of the field of view, and a 
line supposed to be drawn from the eye to the heavens, or really drawn to 
the picture in that direction, marks the true vanishing point. 

It is explained now, why in a long arched tunnel, a bridge, or a cathedral 
with many longitudinal lines on its floor, walls, roof, &c, all such lines seen 
by an eye looking along from one end, appear to converge to a point at the 
other, like the radii of a spider's web ; and why in the representation of a 
common room, viewed from one end, all the lines of the corners, tops and 

bottoms of windows, floors, stripes 



Fig. 230. 




on the carpet, corners of tables, &c, 
being parallel to each other, tend to 
the same vanishing point as V, and 
are cut off by fore-shortening. The 
most important vanishing point in 
common scenes is the middle of the 
horizon, called by painters, the hori- 
zontal line. ; this in a picture, prop- 
erly placed, is at the exact height 
of the eye. It is marked S in Fig. 
229, and V in Fig. 230. Because in 
houses, the roofs, foundations, floors, 
windows, &c, are all horizontal, 
the vanishing points of their lines 
must be somewhere in the horizon ; 
and if the spectator be in the middle of a street, or of a building, and be look- 
ing in the direction of its walls, their vanishing point will be in the center 
of the scene or picture ; if he be elsewhere, it will be at one side. In hold- 
ing up a picture frame, through which to view a scene suitable for a picture, 
it would be proper to raise it until the line of the horizon appeared to cross 
at about one third from the bottom; — this fact becomes the reason of the 
rule in painting, so to place the horizontal line. In beginning a picture, this 
line is usually the first line drawn on the canvass, as marking the place of 
the vanishing points of all level lines and surfaces. And the eye of the spec- 
tator is supposed to be placed in the middle of it, and generally about as far 
from the picture as the picture, itself, is long, such being the extent of view 
which the eye at one time most conveniently commands. 

588. Dr. Arnott* justly remarks, that "much of the delight 
which the art of painting is calculated to afford, is lost to the world, 

* The preceding remarks on Perspective are, with some variation, mostly 
taken from Arnott's " Elements of Physics." 



587. Method of ascertaining the vanishing point in a scene or picture. 
Why lines in a bridge, &c. when seen at one end seem to converge at the 
other. Horizontal line. The first line usually drawn on a picture. Man- 
ner iu which a picture should be viewed. 

588. Dr. Aruott's remarks about the proper manner of looking at a pic- 
*nre. 



LIGHT AM) SHADE, 229 

because persons, in general, know not how to look at a picture. 
Unless the spectator place himself where he can see the objects 
in true perspective, so that he may fancy himself looking at them 
through a window or opening, everything must appear to him false 
nm\ distorted. The eye should be opposite the point of sight of 
the picture, and therefore on a level with the horizontal line, and 
it should be at the required distance, or about the length of the 
picture." 

II. Light and Shade, or the effects of color and distinctness of outline 
upon the appearance of objects in a landscape or picture. 

589. The apparent distance and magnitude of objects is affected 
by distinctness of outline and brightness of color ; or intensity of 
light and shade. 

The painter represents distant views by faint shades, and indis- 
tinct outlines. By deepening the shadows, or heightening the 
colors of a distant mountain, it seems at once brought nearer to the 
view, and the effect of distance is destroyed. Experience has 
thus taught us to associate the idea of distance, with faintness of 
coloring. 

Light radiating from a center becomes rapidly weaker as the 
distance from this center increases. In looking upon a landscape 
illuminated by the sun, we see near objects, such as the flowers, 
fruit and foliage around us, distinct in outline, and glowing with 
bright hues. Strong lights and dark shadows prevail here. As 
the eye extends its range of vision, small objects are no longer 
visible ; there is a blending of colors and of figure until at last 
the outline of the distant mountain or ocean fades away into the 
b'ue sky. 

590. By the proper disposition of light and shade, and the man- 
agement of colors combined with perspective, the painter is able 
to give a good representation of nature. Among the Chinese who 
are ignorant of perspective, pictures are figures of objects drawn 
on the same scale, and with a uniform vividness of coloring, whe- 
ther the objects are supposed to be near or distant ; their only way 
of representing distance, being to carry objects higher up the pic- 
ture, as is done in the attempts at painting of children and untaught 
persons. 

The art of fore -shortening in drawing, and of reducing the size 
of objects as they are more distant, is called linear perspective. 
The varying of color and the disposition of light and shade is called 

539. Effect of light and shade. 

590. How is the painter able to represent nature ? Defect in Chinese 
piciures. Linear perspective. 



230 



NATURAL PHILOSOPHY. 



aerial perspective. The knowledge of the effect of light and shade 
in painting is called chiaro-oscuro.* 

591. The effect of increased or diminished light in making objects appear 
near or remote, is obvious. When a fire breaks out in the night, it appears to 
a distant spectator, as if it were very near ; and he often, for this reason, feels 
needlessly alarmed for the safety of his own dwelling. The bright, red glare 
reflected from surrounding objects brings them nearer to his eye, and he sees 
the firemen with their engines, and others running to and fro, in the bustle of 
the frightful scene, as if almost before his own door. The seaman beholding 
distant mountains suddenly illumined by a bright sun, deems himself near to 
the Jand. Again the sun is obscured, and the coast seems to have receded 
from him. Objects appear larger when seen through a foggy or misty at- 
mosphere. This is owing to the diminished intensity of light which makes 
them appear more distant without diminishing the visual angle subtended by 
them ; for to the man at forty rods distance, who subtends the same angle 
as the one at twenty rods distance, the same object must appear twice as 
large. 

Thus, in the dim twilight, objects seem magnified : the illusion heightened, 
by terror in the minds of the superstitious, readily converts a guide-board 
into a giant ; — passing a church-yard in the night when the atmosphere is 
charged with vapors, fears may readily combine with the optical deception 
produced by such an atmosphere, and cause the white monuments to appear 
as colossal spectres, and the sapling willow with its pensile branches wa- 
ving in the breeze, to seem like a huge monster tossing its arms to and fro. 
Many a ghost-story has arisen from appearances, which the ignorant, not un- 
derstanding, have deemed supernatural. Strange lights which, as they sup- 
posed, warned them of some coming event, might, by a knowledge of the 
laws of optical reflection, have been traced to a candle at a neighboring win- 
dow, or in the range of a mirror, which itself unseen, reflected light upon a 
wall. 



III. Divergence of the Rays of Light ; and Convergence of the 
Optic Axes. 

592. Divergence of the rays of light assists in enabling us to 
judge of the distance or magnitude of objects. Suppose E F to 

be the pupil of the eye, 
Fig. 231. 
E 



it 




and light entering 
from an object at a. 
The rays spread with 
a large angle, or are 
more divergent than 
those from an object at 
b. At c and d the rays 



* Italian words signifying clear and obscure, pronounced Tcearo-scuro. 



591. Examples of the effect of increased or diminished light. A fire seen 
in the night. Distant mountains illuminated by a bright sun. Effects of a 
foggy atmosphere. Of twilight. Optical illusions. 

592. Effect of divergence of light in enabling us to judge of distance. 
Painting cannot give this effect. Convergence of the optic axes. In what 
casp greatest. 



LIGHT UPON TIIK BTK, 231 

are still less divergent. In order to form an image on the retina, 
the eye must make an effort to bend, or refract the rays, exactly in 
proportion as they are divergent when they tall upon the crystal- 
line lens ; and the degree of effort thus made becomes a kind of 
measure of the distance and magnitude of the object. Painting 
cannot give this effect, for while in nature every object, according 
to its distance, is sending rays which meet the eye with different 
degrees of divergence, the rays from a picture coming from a single 
plane surface, have, in every part, the same divergence. The eye 
is not required to exercise the same effort of refracting the rays in 
accommodation to different distances ; and this, in some measure, 
destroys the illusion that painting might otherwise cause. 

By the convergence of the optic axes, we mean that the axis of 
each eye is directed towards one point, or that the two axes con- 
verge when both eyes are looking towards the same point. The 
optic axis is the axis of the crystalline lens continued to the object 
of vision. This imaginary axis back of the crystalline lens termi- 
nates at the middle of the retina, which is called the point of dis- 
tinct vision. The inclination or convergence of the optic axes is 
greater for near objects than for distant ones. 

Thus suppose E and F, (Fig. 231,) mark the places of the two 
eyes ; if directed towards an object at a, it is evident that the two 
optical axes must have a greater convergence than if the eyes were 
directed towards b. When we look at very distant objects, the 
axes of the eyes seem parallel, and we cease to judge of distance 
by their convergence. 



LECTURE XXXVI. 

DURATION OF IMPRESSIONS UPON THE EYE. SINGLE VISION. IM- 

ERFECTION OF VISION. OPTICAL INSTRUMENTS. SHADOW. 

Duration of the Impression of Light upon the Eye. 

593. If a stick burning at one end, is whirled by the hand, a 
circle of light is seen marking its path. As the burning end of 
the stick can only be in one point of the path in the same instant, 
it is manifest that the impression of its light continues on the eye 
after the object has left particular points from whence it was seen. 



593. Examples to prove that the impression of light upon the eye remains 
after the object which produced it is removed. 



232 



NATURAL PHILOSOPHY. 



Fig. 232. 




It has been found that the light of a live coal, placed at the distance 
of 165 feet, continued its impression on the eye during the seventh 

part of a second. 

A toy called the thaumatrope* has been 
invented to illustrate this phenomenon. Fig. 
232 represents a circular card, on one side 
of which there is drawn any object, as a 
carriage, and on the other, a man, in the 
attitude of driving. When the card, by- 
means of strings affixed to it, is twirled 
round with some degree of velocity, the 
carriage and the driver appear as one 
picture. As one side must be out of sight 
while the other is towards us, it follows, 
that we see at once what is drawn upon 
both sides of the card, in consequence 
of the duration of the impression of light on 
the retina, when the object from which it 
proceeds is removed. 

Cause of Single Vision with Two Eyes. 

594. In consequence of the power of directing the axes of 
both eyes in one direction, or of the convergence of the optic axes, 
the mind sees but a single object, though an image is formed 
on each retina. This singleness of vision would take place if, in- 
stead of two, we had a much greater number of eyes ; that is, sup- 
posing they could all direct their axes to the same point. By press- 
ing one eye aside, when we are looking at any object, the axis is 
turned away from its line of inclination towards the axis of the 
other eye, and we see a double image. Images formed at the 
same time, of an object nearer to, or farther from the eye than the 
point where the axes meet, must appear double, because they are 
not formed at the point of distinct vision. 

Supposing the point of distinct vision 
to be a a, in the center of the retina, and 
that the axes are directed towards the ob- 
ject at b , the image is seen single. But 
without changing the direction of the 
axes, attempt to look at an object be- 
yond b, as at c, and the image on each 
eye will be formed outside the point of 
distinct vision, and will be seen double. 
On the contrary, attempt to look at an object at o, while the axes are direct- 
ed towards b, and the image will be formed inside of the point of sight, and 
also appear double. A simple experiment will illustrate this. Hold the two 
fore fingers in aline from the eyes, so that one may be a little more distant 
than the other, by looking at the more distant the nearer will appear double, 



Fig. 233. 




and by looking at the nearer, the more distant will appear double. 
* From two Greek words signifying to learn wonders. 



_ 594. Why is it, that with two eyes, we see objects single 
tinct vision. 



Point of dis- 



VISION. 



233 



595. When the crystalline lens has ceased to be homogeneous, 
either from disease or age, small images, such as the letters of a 
book, will be seen double. Double vision is sometimes apparent 
in persons who are dying ; it is also often occasioned by madness 
or intoxication. Many animals, as lizards, and fishes, and some 
birds, never see objects with more than one eye at a time. Some 
species of fish can only see such objects as are situated above 
them. 

Imperfection of Vision, 

596. When both eyes do not seem to be directed to the object 
at which a person is looking, he is said to be squint-eyed. Short- 
sightedness arises from too great a convexity of the crystalline lens, 
in which case, the rays of light are converged so much that they are 
brought to a focus before reaching the retina. Let D represent 
the crystalline lens, with pencils of light from A B falling upon it ; 

Fig. 234. 




they are collected into a focus at F ; from this point the rays pro- 
ceed in a diverging manner, and form at the retina a b, a confused 
image. By bringing the object viewed near to the eye,, as is done 
by short-sighted persons, the rays fall upon the eye more diverging, 
and are not so soon converged by the crystalline lens, so that the 
focus will fall upon the retina ; for the nearer an object is brought 
to a lens, the farther the image recedes from it. 

Short-sighted people are assisted by concave lenses ; the effect 
of such lenses being to diverge rays of light. Thus the glass A B 

causes the rays whicji 
Fig. 235. fall from the object o, to 

Js. «s=»o become more divergent ; 

and the crystalline lens 
C D, which is too con- 
vex, then converges the 
rays, and the image or focus is thus thrown as far back as the re- 




595. Different causes of double vision. 

596. Squinting. Short-sightedness. Why do the short-sighted bring ob- 
jects very near to the eye ? Effect of concave lenses in assisting vision. 

20* 



234 NATURAL PHILOSOPHY. 

tina R. Without the aid of concave eye-glasses, near-sighted 
people cannot see objects at a little distance with any distinctness. 
As age advances, the eye becomes flatter^ and this often enables 
those who were near-sighted in youth, to see without the aid 
of glasses of any kind. 

597. Long-sightedness arises from a want of sufficient convexity 
in the crystalline lens. As age advances, the eye becomes flat- 
tened in consequence of the decay and shrinking of the refracting 
humors. This change is denoted by a tendency to hold a book at 
a greater distance when reading ; for as the rays of light are 
not converged by the flattened crystalline lens sufficiently to 
bring them to a focus on the retina, this focus, or the image 
of the object is formed at a point beyond. A convex lens inter- 
posed between the object and the eye, by bending the rays to a 
greater convergence, brings the focus forward, and the image is 
formed on the retina. Thus the spectacles worn by aged persons 
are usually convex lenses. They do for the eye that portion of the 
labor of bending the rays of light, which it has not the ability to 
perform for itself. The functions of the eye being thus aided, the 
benefits of sight are secured to those who advance in years. 

Let C D represent the 
Fig. 236. crystalline lens of the 

eye, and A B a convex 
glass or spectacle lens ; 
the object o, at about six 
inches from the eye, will 
form a perfect picture of 
the object at R, the retina. But if the lens A B be removed, the 
image will be confused, and it will be necessary to withdraw the eye 
to three or four times the distance, and if it be a minute object, 
the unassisted eye may not be able to distinguish it at any distance. 

598. The cataract is a disease occasioned by the crystalline lens losing its 
transparency. This opacity, if total, prevents the passage of rays to the re- 
tina; if partial, it renders the image there formed, very dim and indis- 
tinct. The operation, or couching, for the cataract, consists in taking 
the defective lens or humor from the eye, in which case light can again re- 
visit the " dim orb." But the principal converging power being gone, the 
image, instead of being formed on the retina, will be at a point beyond it. 
A convex, artificial lens here answers the purpose of the natural one. Thus 
persons who have undergone the operation of couching for the cataract, 
usually wear very convex spectacles. 

Optical Instruments, 
599. The ancients appear to have been better acquainted with 

597. Cause of long-sightedness. Indication of this defect. Effect of a 
convex lens where the eye is too flat. 

598. Cataract and its remedy. 

599. O.ptical glasses used by the ancients. 




OPTICAL INSTRUMENTS. 235 

mirrors, or glasses for the reflection of light, than with lenses, or 
glasses tor its refraction. The burning mirrors of Archimedes 
were named in history two hundred years before the Christian era. 

600. Spectacles are lenses mounted upon a metallic frame so 
that they can be conveniently worn before the eyes. The spec- 
tacles worn by aged people are convex lenses; they assist the 
flattened, crystalline lens of the eye to converge the rays of light. 
The common eye-glasses carried by near-sighted people, are con- 
cave lenses, which counteract, by their divergence, the effect of too 
much roundness of the refracting lens of the eye. It is not ascer- 
tained by whom spectacles were invented ; they were not in use 
before the thirteenth century, though the magnifying power of con- 
vex lenses was understood at an earlier period. 

601. The microscope* is designed to assist the eye in viewing 
minute objects. — A double convex lens, or small globe of glass, is 
the simplest kind of microscope. When applied to small objects, 
as the stamens or pericarp of a plant, the surface of a crystal, or the 
letters of a book, it exhibits parts not visible to the naked eye, or 
magnifies such as are visible. Without the aid of the microscope, 
we cannot view objects distinctly if held nearer to the eye than 
three or four inches. For when an object is brought nearer and 
nearer to the eye, we at length reach a point, within which, sight 
becomes confused. This point is called the limit of distinct vision, 
and varies a little in different persons. The cause of this confusion 
of sight is, that the divergence of the rays of light from a near ob- 
ject, is too great for the refracting power of the crystalline lens of 
the eye to collect them, to form an image on the retina. 

If an object be placed within an 
Fig. 237. inch or two of the eye, the rays 

which proceed from it are too di- 
yt vergent to be refracted so as to 

form a focus on the retina. But let 
the same object be viewed, at the 
same distance from the eye, by the 
assistance of the " convex lens B, 
whose focal distance is B A ; those 
rays diverging from the object which 
fall on the surface of the lens, will 
be refracted at its two surfaces, and 

* From the Greek micros, minute, and scopio, to see. 

600. Spectacles. Eye-glasses. 

601. Use of the microscope. Simplest kind of microscope. How does 
the microscope enable us to see objects nearer to the eye, than when the 
vision is unassisted 1 Why does the microscope magnify objects? Effect 
of looking upon the letters of a book through a pin-hole made in paper. 




28fi NATURAL PHILOSOPHY. 

emerge from it nearly parallel to each other, consequently the ob- 
ject is capable of being viewed by the eye on the side B, under a 
greater angle than it could be seen without the lens. And, be- 
cause the object is seen under a greater angle, it is magnified ; 
and minute portions, which were before invisible because they did 
not occupy sufficient space on the retina, are now brought into 
view. Even by looking through a pin-hole in a piece of colored 
paper, the letters of a book will appear larger, and more distinct, 
than when seen in the ordinary way. This greater distinctness is 
owing to the exclusion of the diverging rays r r, of each pencil of 
light, which falling obliquely upon the eye, are not brought to the 
focus with the central rays, and therefore tend to confuse an image. 
The smallness of the pin-hole allows only the axes of the several 
rays to pass, and these proceed in lines almost parallel. Through 
such an aperture, letters appear very large and distinct, when a 
book is held within an inch of the eye. On removing the perfo- 
rated paper, and attempting to look at the letters at the same dis- 
tance as before, there is no distinct vision. 

602. The single microscope consists of a convex glass called a 
magnifying glass, in the focus of which, is the object. By means 
of the converging power of the magnifier, the eye may be brought 
very near the object. The rays from the object at O being bent 

at A B, proceed to the pupil 
Fig. 238. C, and fall on the crystalline 

lens, D, in such a manner, as, 
A. y^ _^:^%v when again refracted, they 

form a magnified image on the 
retina RR. The more con- 
vex a lens is, the shorter is its 
focus ; and the shorter the fo- 
cus of a lens, the greater is 
its magnifying power. 

603. It is important, for many purposes, to know the exact mag- 
nifying power of a microscope ; that is, whether it makes an ob- 
ject appear ten, fifty, or a hundred times larger, than when view- 
ed with the naked eye. This magnifying power depends on the 
difference of the distance of the object from a lens, and the distance 
when seen without its assistance ; or, in other words, on the ratio 
between the focal distance of the lens, and the limits of distinct 
vision. This latter point varies in different persons, and at dif- 
ferent periods of life in the same person. In reading, the most 
common distance at which we hold a book from the eyes, is, proba- 

602. Single microscope. 

603. On what the magnifying power of a microscope depends. Focus 
of the eye, or points of distinct vision. 




MICKOSCOPE. 



237 



bly about ten inches. When we examine the different parts of a 
flower or an insect, we hold the object nearer. 

G04. The compound microscope consists of two, 
Fig. 239. or more, convex lenses, one of which, called the 

object-glass, is used to form an enlarged image 
of the object, and the other, called the eye-glass, 
to magnify the image. In the single micros- 
cope the magnified object is seen ; in the com- 
pound microscope the object is not seen, but its 
magnified image. Suppose an object a b, to be 
placed a little beyond the focus of the object-glass 
c d, the rays of light proceeding from it will be 
collected on the other side of the lens and form 
an enlarged and inverted image at g h. The 
eye-glass e f, again magnifies the image which 
is formed on the retina at A B, in an upright 
position. 

605. The solar microscope is so named, be- 
cause the object is illuminated by the solar light, 
reflected from a plane mirror. It has two lenses 
contained within a tube which, when the micro- 
scope is used, is placed in a hole in the window- 
shutter of a darkened room. The reflector is placed outside the 
shutter, to receive the solar rays ; these fall upon a large convex 
lens called a condenser, whose office is to collect the rays, and 
throw them upon an object placed within its focus. These rays 
are again refracted, and form behind the second lens, a magnified 
image of the object which is thrown upon a screen. Let P Q, re- 
present the reflector of a solar microscope S, incident rays which 

Fig. 240. 





604. Parts of the compound microscope. Explain the manner in which, 
objects are viewed through a compound microscope. 

605. Solar microscope. Explain the manner in which the solar micro- 
scope is used. Discoveries made by means of the solar microscope. 



238 ' NATURAL PHILOSOPHY. 

being reflected upon the condenser, or the lens X Y, are converg- 
ed and brought to a focus at A B. The object being placed at 
this focus, reflects the concentrated light from its surface, in all 
directions, the rays which fall upon the lens C D, are refracted 
and form the magnified image E F, upon a screen, or the wall of 
an apartment. 

The solar microscope has opened a new field of wonders. The common 
microscope had previously done much towards revealing the fact, that man 
lives in a world, of which, he knows, comparatively, little. The young stu- 
dent iu natural history, who, for the first time, examines an insect through a 
microscope, is astonished at the transformation of a fly into a huge monster, 
with eyes of fire, and a proboscis like an elephant ; or, at seeing in a piece 
of wood, regular hexagonal divisions, as large as the cells in a honey-comb. 
The solar microscope has shown the existence of life where it had not before 
been suspected. The fine dust upon a fig or the rind of a cheese, when ex- 
amined through this instrument, is seen animated with creatures scrambling 
about like pigs among rocks ; and a drop of vinegar appears like an ocean 
filled with sea-monsters. Of all the wonders exhibited by means of the solar 
microscope, the process which takes place in the crystallization of salts, is, 
perhaps, the most striking ; where particles of matter not gifted with intel- 
ligence or even life, are seen taking their respective place to form a cube or 
prism, with as much precision as a company of soldiers form themselves into 
a phalanx or platoon. 

606. In the magic lantern the light of a lamp is substituted for 
solar light. This instrument is a microscope ; but instead of be- 
ing used to magnify natural objects, it is commonly employed to 
give a magnified representation of pictures. Though often em- 
ployed for amusement, it is very useful in illustrating lectures on 
scientific subjects particularly astronomy. The objects to be re- 
presented are painted on small thin plates of glass, which being 
transparent, colors as well as forms are represented. The magic 
lantern consists of a tin box containing a lamp, behind which is 
placed a metallic reflector. In front of the lamp is a plane con- 
vex lens which receives on its plane surface the reflected light of 
the lamp, and concentrates it on the object ; this is magnified by 
another lens fitted to the extremity of a tube projecting from the 
lantern. The paintings are passed through a narrow opening in 
the tube, between the lenses. The experiment is to be performed 
in a dark room, with a white wall or screen, on which the magni- 
fied and illuminated image is cast. The farther the lantern is 
withdrawn from the screen, the greater the image will appear, 
though it may be indistinct by being too far removed. In 
order that the image may be seen erect, the object must be 
inverted. 



606. Construction of the magic lantern. 



CAMERA OBSCU11A. 



239 



Fig. 241, 




A, the magnifying 
lens. 

B, the object intro- 
duced through an o- 
pening in the tube. 

C, the condensing 
lens. 

D, the lamp. 
J3, the concave mir- 
ror. 

F, the image thrown 
on a screen, or a white 
wall, in a dark room. 
a, a thumb-piece, 
by which the magni- 
fier may be made to 
approach to or recede from the object, and thus the image be thrown to a greater 
or less distance, according to the magnitude required. 

607. Another optical instrument is the camera obscura.* The 
eye is a camera obscura where light from without, enters a dark 
chamber by means of a small aperture called the pupil of the eye, 
and being refracted by the convex crystalline lens, forms an image 
on a screen behind it, viz., the retina. 

Let C D represent a darkened chamber, or large box with an aperture at L, 
where is fixed a convex lens of such a curvature that the focus of parallel rays 
falls upon the opposite wall. The object A B being at a suitable distance, an 

inverted image will be formed on a 
screen or on the opposite wall. The 
pencil of light which proceeds from 
A will converge to a, the pencil from 
B will converge to C, and the inter- 
mediate points of the object will be 
reflected between a and C. The 
picture is viewed from an opening in 
the top of the box. If the chamber 
had a soul, and a communication by 
some contrivance like that of the 
optic nerve, could convey to it the 
image formed, then the chamber, or 
rather the soul within it, could see. 
But the image on the retina or the 
screen is inverted ; — and does the 
soul within the chamber see things 
upside down? Some philosophers 
have asserted that this is the case, 
and that experience teaches the child 
to regard objects in their true posi- 
tion. But let us in the first place 
consider that the soul has no mate- 



Fig. 242. 




Literally, a dark chamber. 



607. Resemblance between the camera obscura and the eye. Are objects 
in reality seen by the eye in an inverted position 1 Construction of a camera 
obscura. 



240 



NATURAL PHILOSOPHY. 



rial eyes, and, therefore, that there can be no analogy between mental and 
bodily vision ; and secondly, if the soul were behind the screen, and looking 
down upon the inverted picture (like the man in the figure,) the objects there 
delineated would appear in their true position. 

608. Telescope. The microscope and telescope* are used for 
very different purposes, the one to examine minute objects, placed 
very near to the eye, and the other to view large and distant ob- 
jects. The telescope does indeed make use of the microscope in 
its operations, or rather an image is first formed of a distant ob- 
ject by means of a convex lens or a concave mirror, and then 
viewed and magnified with a microscope. In a refracting tele- 
scope the image is formed by means of a convex lens. In a reflect- 
ing telescope the image is formed by means of a concave mirror. 

The astronomical telescope consists of two convex lenses, an 
object-glass, and an eye-glass. 

The object-glass is directed towards the object. The eye-glass 
is at that end of the instrument at which the eye is applied. 

Suppose A B to 
Fig. 244. 
C 



represent rays from 
some distant object, 
as a star, then the 
image formed by the 
object-glass C, be- 
ing viewed through 
the eye-glass G H, will be magnified according to the magnifying 
power of the lens G H. Thus if the object-glass have a magni- 
fying power equal to 10, and that of the eye-glass of 6, the object 
will be magnified 60 times, or 10x6. The image will be invert- 
ed ; this is not an important defect, because the use of this tele- 
scope is confined to observations of celestial bodies. 

609. Terrestrial telescopes, used for ship, and spy-glasses, are 
less simple than astronomical telescopes, having two additional 
lenses in order to obtain erect views of the object. 

Thus A B, the object-glass, forms an inverted image n m of the 
object M N. In the astronomical telescope this image would be 
viewed at L. But the pencil of parallel rays here crossing each 

Fig. 245. 

c 





* From two Greek words, the meaning of which is to see at a distance. 



608. Difference between the microscope and telescope. Astronomical 
telescope. 

609. Terrestrial telescope. 



SHADOW. 241 

other falls upon the lens E F, (which is of the same focal length 
as CD;) this lens collects the rays into a focus where the erect 
image m n appears. This image is viewed by the eye at E by 
means of the eye-glass G H. The additional lenses E F and C D 
do not magnify, their focal length being the same as that of the 
eye-glass G H. Were they smaller, or more convex for the pur- 
pose of magnifying, the light would be injured and the field of view 
limited. 

610. The reflecting telescope has two concave metallic mirrors, 
with two plano-convex eye-glasses. 

611. The telescope magnifies as many times as it presents ob- 
jects under an angle greater than is presented to the naked eye. 
The moon, for example, appears to the naked eye under an angle 
of half a degree; consequently a telescope magnifies 100 times, 
when it represents the moon under an angle of fifty degrees. If 
it were made to magnify 180 times, it would represent the moon 
under an angle of 90 degrees, in which case the moon would ap- 
pear to fill one quarter of the heavens. 

Euler, a celebrated German philosopher wished, as the thing, of all others, 
most desirable, that he had a telescope which would magnify 100,000 times, 
so tbat he could see the moon as if only half a mile distant, and observe the in- 
habitants and animals which may be upon it. But the little boy might with 
equal propriety wish his rocking horse were alive, and the little girl that her 
doll would talk, as philosophers amuse themselves with wishes that can never 
be accomplished. There are limits to human efforts ; and it is not probable 
that men will ever build a tower high enough to reach the heavens, or construct 
a telescope which will make us very near neighbors to any of the celestial orbs. 
The great telescope of Sir William Herschell, was four years in building; it 
was forty feet in length, and the great mirror was four feet in diameter ; it 
magnified 6000 times. Its focal length was forty feet. The star Syrius, when 
viewed through this telescope, appeared of the size and brilliancy of the sun. 
By its means a sixth satellite of Saturn was discovered, the day on which it 
was completed. Improvements in optical instruments have rendered an appa- 
ratus so very cumbrous, the less necessary, by combining, in a smaller com- 
pass, greater advantages than were possessed by this. 

612. Shadow. For the formation of a shadow two things are 
necessary ; 1st, a luminous, and 2d, an opaque body. The opaque 
body interrupting the passage of the rays from the luminous body, 
causes darkness beyond it, and this produces upon a wall or screen 
what is called a shadow, it being, in reality, a dark image of the 
opaque object. Darkness is merely the absence of light, as cold 
simply denotes the absence of heat. 

613. There are three things to be observed with respect to the 
form and size of shadows : 1st. Where the luminous body is smaller 

610. Reflecting telescope. 

611. Cause of the magnifying power of the telescope. Herschell's tele- 
scope. 

612. Cause of shadow. 

613. Cause of difference in the form and size of shadows. 

21 



242 



JVATUKAL PHILOSOPHY. 



Fig. 246. 




Fig. 248. 




than the opaque body. 
Let L be a luminous 
body, smaller than the 
opaque body O. It is 
evident from the diverg- 
ing of the rays, that the 
shadow will be larger 
in proportion to its dis- 
tance from the object. 
When the luminous body 
is larger than the opaque body. 
Thus let A be a luminous body, 
(the sun) and B an opposite 
body, (the earth,) the shadow 
will be in the form of a cone, 
and will gradually diminish in 
size till it terminates in a point. 
3d. When the luminous body 
is of the same magnitude as the 
opaque body. Here the shadow 
will be that of a cylinder. Thus 
let A be a luminous body of the 
same magnitude as B. The lines a m and a n are parallel, and if 
the shadow of B were extended to infinity, it would be cylindrical. 
614. The darkness of a shadow is in proportion to the inten- 
sity of light which is interrupted by the opaque body. Though as 
surrounding objects reflect light, the shadow itself will be in some 
measure illuminated. Were it not for this, shadows would appear 
perfectly black. 

A number of lights will 
cause the same number of 
shadows of the same ob- 
ject, unless the lights are 
situated in the same line 
of directi on. Suppose a bail 
A, to receive light from 
C three lamps, B C and D ; 
the light B will produce 
the shadow b, the light C 
will produce the shadow c, 
and the light D the shadow 
cZ, but the shadows will not 
be very dark, because they 






Fi£. 249. 




614. Cause of the different degrees of darkness in shadows, 
several shadows of the same object. 



Cause of 



NATURE OF LIGHT. 243 

receive some light from the two lamps which are out of their line 
of direction. The ball hides the light from the lamp C ; but the 
wall at the place of the shadow c is illuminated by the other two 
lamps. 



LECTURE XXXVII. 



NATURE OI' LIGHT. DECOMPOSITION OF LIGHT. DISPERSION OF 

LIGHT. RAIN-BOW. ABSORPTION OF LIGHT. 

Gl">. The colorless light which proceeds from the sun, is re- 
flected in a variety of colors from the foliage of trees, the petals of 
flowers, and other innumerable objects around us. How beauti- 
ful, how kind, and how wise is this arrangement ! A clear trans- 
parent light meets our gaze when we look upwards or around us 
in space ; but when we look down upon the earth, our eyes are 
feasted by the brilliant and delicate hues which issue from this 
transparent light, as it is decomposed by the objects on which it 
falls. 

Theories respecting the Nature of Light. 

616. There has ever been much dispute respecting the nature of light. The 
ancients asserted that there ?nust be something between the eye and the object 
seen ; for, without some medium there could be no communication. The great 
question was to ascertain what this medium, or this something was. One sup- 
posed " that the eyes, themselves, emit rays, or emanations of some unknown 
kind, by which distant objects are, as it were, felt." This hypothesis was ab- 
surd, because it assigned no reason why objects should not be seen as well in 
the dark as light, or in fact why there should be any darkness at all. Others 
imagined " that all visible objects are constantly throwing off in all directions, 
images, films, or spectral resemblances of themselves, which produce our im- 
pressions of the objects." Aristotle, in accordance with this opinion, supposed 
the mind to reside in the brain, which was filled with the images, or forms of 
ideas as well as things. 

617. Newton, the great founder of the science of optics, rejecting this idea 
of spectra, or resemblances being thrown off by the luminous body, supposed 
that particles of incalculable minuteness, dart, in all directions, from every por- 
tion of the surface of luminous bodies ; and that these particles are subjected to 
the laws of attraction and repulsion. Attributing to light these properties of 
matter, he believed light, itself, to be material, and that its particles were turn- 
ed aside so as never to come in actual contact with the particles of the bodies 



615. Reflection the cause of colors. 

616. Opinions of the ancients respecting the nature of light. Aristotle's 
opinion. 

617. Newton's theory. 



244 NATURAL PHILOSOPHY. 

on which they fall ; but either being turned back and reflected by the repulsive 
forces before they meet them, as in the case of opaque bodies, " or penetrating 
between their intervals, as a bird may be supposed to fly through the branches 
of a forest and undergoing all their actions, to take, at quitting them, a direc- 
tion according to the position of the surface at which they emerge with respect 
to their course."* Newton's theory is called the system of emanation, it being 
imagined that rays of light emanate from the sun, as water issues from a 
fountain. 

618. Another theory with respect to the nature of light seems, at the present 
day, to be in favor with many eminent writers. This supposes " light to be 
produced in the same manner as sound, by the communication of a vibratory 
motion from the luminous body to a highly elastic fluid," called ether, which 
fills all space. Thus instead of anything being actually thrown off, this theory 
supposes light to depend on vibrations or undulations of ether, caused by that 
luminous body, as sound depends on pulsations of air produced by the sonorous 
body. 

There are strong objections to this theory. In the first place, it supposes a 
substance, (ether,) which we do not know to exist ; and it is contrary to the 
rules of sound philosophy, thus to refer to a cause of which we have no know- 
ledge ; and secondly, its explanations of various phenomena of light are neither 
so simple nor so satisfactory as by the Newtonian theory. Still there are ana- 
logies so close between sound and light, that there is some plausibility in refer- 
ring them to analogous causes. 

619. One of the great advocates for the theory of vibrations, Euler, after as- 
serting the existence of a subtle medium which pervades all space, says, " As 
the vibrations of air produce sound, the vibrations of ether produce light. The 
rays of light consist in the shapes and vibrations transmitted by the ether, as 
sound consists in the shakings or vibrations transmitted by the air. The sun 
then loses nothing of his substancet in this case, any more than a bell does in 

* The learned Sir John Herschell, who is not a disciple of the Newtonian school, in re- 
spect to the nature of light, thus humorously illustrates Newton's doctrine of refraction ; but 
truth may be uttered in jest, and those who believe in the system of emanation, may thank 
Sir John for his apt and lively simile. 

j The fears which some Philosophers seem to entertain lest the sun will, in process of 
time, part with all its light, seems to show hut little confidence in the providence of Him who 
spake light into existence ; — why do we not fear lest the fountain of rivers will he dried, or 
lest the northern and southern portions of the globe will he left without an atmosphere, since 
the air is continually rushing from thence towards the equator? We know that God has pro- 
vided means for a constant renewal of the fountains by evaporation, and that there are in the 
upper regions of the atmosphere supplies of air going to restore the equilibrium. Thus 
the sun which bestows light upon all bodies within its system, may in return, by some pro- 
cess analogous to evaporation, draw from the opaque planets of its system, the elements of 
which light is composed, (for it is evident that light is a chemical combination of various ele- 
ments.) Everywhere in nature we perceive a system of compensations ; the plant yields to 
the animal the vital element, and the animal in breathing sends forth the substance which 
alone can give life and vigor to the plant. Shall we say, we do not understand how God can 
replenish the lamp he has set in the heavens, and thereforewe will not believe his own as- 
sertion, "that he gave the sun to rule the day?" but the rather admit that every object 
which seems to reflect light is in motion, and that light, itself, is nothing but undulations of a 
supposed medium which all these vibrating objects put into motion. Instead of the sublime 
passage, " God said let there be light, and there was light," we should read, " and God 
said, let everything begin to vibrate, so that there may be an appearance of light." But 
we are met by another difficulty ; — at the period when the scriptures inform us light was cre- 
ated, there had been nothing else formed, and therefore there could be no vibratory bodies. 

618. Theory of vibrations. Objections to this theory. 

619. Euler's remarks with respect to light and sound. Comments of Eu- 
ler upon Newton's theory of light. Opaque bodies compared to musical in- 
struments. Colors accounted for on the system of vibrations. Leading doc- 
trines of optics firmly established. 



DECOMPOSITION OF LIGHT. 245 

vibrating." Nowton's theory of the reflection of light from opaque bodies, is 
thus commented on by Euler. " We see opaque bodies themselves, but not the 
images of the luminous bodies which enlighten them, as must be the case if we 
see them by the refraction of their surface." Euler considers that an opaque 
body when illuminated, is in a state of vibration in its minuter particles, caused 
by the more powerful vibrations of the luminous body. " Opaque bodies," he 
says, " as long as they are not illuminated, must be compared to musical instru- 
ments not in use, or to strings which emit no sound till they are touched." 
Again he says with respect to colors, " as in music, flat and sharp notes de- 
pend on the quickness of vibrations, a similar difference in the vibrations of the 
rays of light must produce as important an effect on vision. It is this effect 
which causes diversity of colors ; that is, difference of color is to the organ of vis- 
ion, what flat or sharp sounds are to the ear." Thus according to the system 
of vibrations or undulations, every simple col6\ depends on a certain number of 
vibrations which are performed in a certain time ; so that this number of vibra- 
tions made in a second, produces that sensation which belongs to the red color, 
another number of vibrations produces the sensation of yellow, another of 
green, &c. 

But we have wandered too long in regions of speculation. It is our object 
to teach truth, deduced from facts that have been learned from observation, 
or may be demonstrated by experiment. Fortunately neither the theory of 
emanation, nor that of vibration, can overthrow the science of optics, which, 
not being built upon the doubtful foundation of any hypothesis, need not, of ne- 
cessity, stand or fall with it. We may add, too, that though Newton's disco- 
veries were explained in language consonant to his own peculiar opinions, this 
language is still used, even by those who reject these opinions. We shall pro- 
ceed to explain the nature of colors as first proved by this Philosopher by means 
of the prism. 

620. Decomposition of Light. Light is not a simple substance ; 
this is proved by the fact that the white light which comes from 
the sun, or any other luminous body, may be decomposed. 

Experiments showing the compound nature of light are usually 
made with the prism, a triangular piece of glass, peculiarly fitted, 
by its shape, for refracting the rays of light. " The optical prism, 
is usually understood to be a piece of solid glass, having two sides 
constituted of equal parallelograms, and a third side called the 
base. The line of intersection of the two sides is called the edge, 
and the angle contained by the sides, the refracting angle of the 
prism. A straight line passing lengthwise of the prism, through 
its center of gravity, and parallel to the edge is called the axis. 
A section made by a plane perpendicular to the axis, is an isosce. 
les triangle. Frequently, the three angles of the prism are made 
equal to one another, each being 60°. 

We do not read in Holy Writ that God created sound, but we find sound in various places 
ascribed to the agency of air, and other media ; thus the expressions, a rushing wind, the 
sound of waters, &c. ; we do not indeed consider the Bible as a system of physics; there are 
many sciences to which this Holy Book has no immediate reference, but we think, that as 
light is plainly declared to have been created, a Christian Philosopher should not deny its 
actual existence as a primary agent, especially, when, independently of the Bible, the evi- 
dence preponderates on the other side of the question. 

600. Light, not asimple substance. Explanation of the prism, 

21* 



246 



NATURAL PHILOSOPHY. 



Fig. 250. 




Fig. 250 represents a section of a 
prism ABC, of which AB is the 
base, and ACB the refracting an- 
gle. DE is a beam of the sun's light 
falling obliquely on the first surface 
AC, where one portion is reflected 
but another portion transmitted. — 
The latter portion, instead of pass- 
ing directly forward and forming an 
image of the sun at H, is turned up- 
ward towards the perpendicular p p, 
meeting the opposite surface CB in 
F, where it is again turned upward 
from the perpendicular^ p in the di- 
rection FG, carrying the image of the sun from H to G."* 

621. By means of the prism, Newton proved that light consists 
of seven different kinds of rays, varying in color, refrangibility, and 
other properties. Let a room be darkened, and admit a beam of 
light obliquely through a hole in the window shutter. If this beam 
of light be received upon a screen, f or upon the wall, a luminous 
spot only will appear ; but if a lens be placed before the beam of 
light, the rays will be bent out of their straight forward course, 
and, in this refraction, they will separate and arrange themselves 
in the screen, according to their different degrees of refrangibility. 

E F represents the win- 
dow shutter, H a hole in 
the same, S the beam of 
light, which, if not inter- 
rupted, would go on, in a 
straight line, and form a 
round white spot at P. — 
B A C is a prism, whose re- 
fracting angle is at A. The 
beam of light falling on its 
first surface, C A, emerges 
at an equal angle of refrac- 
tion from its second surface, 
B A, in the direction g G. 
From the ordinary exam- 
ples of refraction, we should 
expect that this beam of 



Fig. 251, 




Yfhite> <*'p 



light, which before fell uponP, would only change its direction, and fall some 
Where upon M N. But instead of a round, white spot, there appears on the 
screen M N, an oblong image K, divided into seven, colored spaces, of unequal 
extent, and arranged in the order represented, beginning with the red. 

* Olmsted. 

t A piece of white paper or the white wall will serve the purpose of a 
screen^ but a sheet of drawing paper fixed to a movable stand is the most 
convenient. 



621. Experiments with the prism colors exhibited in the solar or prismatic 
spectrum. 




HOMOGENEOUS LIGHT. 247 

This image is called the solar, or prismatic spectrum. It will be seen that the 
red ray is nearest the lino P II, in which the light would have proceeded if it had 
suffered no refraction, while the violet is the most distant, from this line ; there- 
fore the red ray is the least refrangible, and the violet ray the most refrangible. 
&2'2. Tho various colored rays of the spectrum may be collect- 
ed by a convex lens, and when the image is received on a screen, 
a circular spot of white light is produced. Thus by synthesis, as 
well as analysis, is proved the compound 
Fig. 252. nature of lights. That the seven colors 

of the spectrum produce white light may 
also be proved by the following experi- 
ment. On a circular card, paint the colors 
in their due proportions ; on turning the 
card rapidly, the colored circle will ap- 
pear white. It will be seen by the figure 
that the width of the violet ray is the 
greatest, being 80°, and that of the or- 
ange the least, being 27° ; green and 
blue occupy each 60° of the spectrum, 
yellow 48°, red 45,° and indigo 40°. 
623. Homogeneous Light. It is asserted by some modern wri- 
ters that there are but three homogeneous or simple colors, viz. ; 
red, yellow and blue. Orange may be made by mixing red and 
yellow ; green, by mixing yellow and blue ; and violet a faint 
shade of indigo, mixed with a little red. 

Sir David Brewster, one of the most popular writers on optics, of the present 
day, thus remarks upon homogeneous light. " Among the wonders of science, 
there are perhaps none more surprising than the effects produced upon colored 
objects by illuminating them with homogeneous light, or light of one color.'* 
After describing the method by which, owing to late chemical discoveries, yel- 
low light may be produced in sufficient quantities for illuminating a room, he 
continues: "Having thus obtained the means of illuminating any apartment 
with yellow light, let the exhibition be made in a room with furniture of various 
bright colors, with oil or water colored paintings, on the wall. The party which 
is to witness the experiment should be dressed in a diversity of the gayest colors ; 
and the brightest colored flowers and highly colored drawings should be placed 
on the tables. The room being first lighted with ordinary lights, the bright and 
gay colors of everything that it contains will be finely displayed. If the white 
lights are now suddenly extinguished, and the yellow lamps lighted, the most ap- 
palling metamorphoses will be exhibited. The astonished individuals will no 
longer be able to recognize each other. All the furniture in the room, and all 
the objects which it contains, will exhibit only one color. The flowers will lose 
their hues. The paintings and drawings will appear as if they were executed 
in Chinese ink, and the gayest dresses, the brightest scarlets, the purest lilacs, 
the richest blues, and the most vivid greens, will all be converted into one mo- 

622. White light produced by collecting the prismatic colors. 

623. Remarks of Brewster upon homogeneous light. Effects of illumina- 
ting objects with homogeneous light. Effect of illuminating with different 
colored light. 



248 NATURAL PHILOSOPHY. 

notonous yellow. The complexions of the parties, too, will suffer a correspond- 
ing change. One pallid death-like yellow, 



-like the unnatural hue 



Which autumn plants upon the perished leaf, 

will envelop the young and old, and the sallow faces will alone escape from the 
metamorphosis. Each individual derives merriment from the cadaverous ap- 
pearance of his neighbor, without being sensible that he is himself one of the 
ghostly assemblage. 

If, in the midst of the astonishment which is thus created, the white lights are 
restored at one end of the room, while the yellow lights are taken to the other 
end, one side of the dress of every person, namely, that next the white light, wiil 
be restored to its original colors, while the other side will retain its yellow hue. 
One cheek will appear in a state of health and color, while the other retains the 
paleness of death, and, as the individuals change their position, they will exhibit 
the most extraordinary transformations of color. 

If, when all the lights are yellow, beams of white light are transmitted through 
a number of holes like those in a sieve, each luminous spot will restore the color 
of the dress or furniture upon which it falls, and the nankeen family will appear 
all mottled over with every variety of tint. 

If red and blue light could be produced with the same facility, and in the 
same abundance as yellow light, the illumination of the apartment with these 
lights in succession would add to the variety and wonder of the exhibition. The 
red light might perhaps be procured in sufficient quantity from the nitrate and 
other salts of strontia ; but it would be difficult to obtain a blue flame of suffi- 
cient intensity for the suitable illumination of a large room. Brilliant white 
light, however, might be used, having for screens glass troughs containing a 
mass one or two inches thick of a solution of the ammoniacal carbonate of cop- 
per. This solution absorbs all the rays of the spectrum but the blue, and the in- 
tensity of the blue light thus produced would increase in the same proportion as 
the white light employed." 

624. Dispersion of Light. It is found that the length of the 
solar spectrum depends on the nature of the prism employed, by 
experiments made with transparent liquid substances of various 
kinds, inclosed within glass plates arranged in a triangular form. 
The oil of cassia, when used as the material for a prism, forms a 
spectrum twice as long as the common glass prism ; it is, there- 
fore, said to have a greater dispersive power than glass. 

625. The difference between dispersion and refraction is very important. 
Newton did not observe that the dispersion or divergence of the different 
colors on the spectrum was greater when produced by one refracting body, 
than by another. He therefore, erroneously concluded, that the refractive 
and dispersive powers of bodies must always correspond. In the construc- 
tion of his refracting telescopes he found much difficulty from the colored 
fringes which rendered the image indistinct. Opticians have now learned 
to correct this defect, by the use of lenses of different dispersive powers. 
Telescopes constructed thus are called achromatic* The eye is an achro- 
matic instrument. Its crystalline, aqueous, and vitreous humors, form lenses 

* From the Greek, a, destitute of, and kronia, color. 



624. What is meant by the dispersing power of any reflecting substance ? 

625. Error of Newton with respect to dispersion and refraction. Defects 
pf Newton's telescopes. How remedied. 



ItAIN-ItOW. 



249 



possessing different dispersive powers, which mutually correct the aberra- 
tions of* each other. 

626. Rain-bow. The rain-bow shows the prismatic spectrum 
on a grand scale, 

" Bestriding earth the grand etherialbow 
Shoots up immense ; and every hue unfolds, 
In fair proportion, running from the red 
To where the violet fades into the sky." 

The rain-bow is caused by the reflection and refraction of light by 
means of drops of water, which produce the effects, both of convex 
mirrors, and convex lenses. It is when the sun may be seen 
shining through falling rain-drops that we see the rain-bow. If 
drops of rain were flat, instead of being round, the rays of light 
would be reflected by them to the earth without being divided into 
prismatic colors, and the rain-bow would appear an arch of glit- 
tering, colorless light. But the spherical drops first bend, or re- 
fract the rays, dispersing prismatic colors, and then reflect them 
in the varied colors, and in the order they are exhibited in the 
prism. 

Suppose A to be a drop of 
rain, and S d a ray of light fall- 
ing upon it at d; it will not go 
to c, but be refracted to n, here 
one part will leave the drop, 
and another part be reflected to 
q, where it will suffer a second 
refraction ; the drop acting as a 
prism, separates (disperses) the 
ray into the colors of the spec- 
trum, the red being lowest, and 
the violet highest, or, in other 
words, the red being least re- 
fracted, and the violet most re- 
fracted. The angle made by 
the red ray with the solar, inci- 
dent ray, that is, the angle S / q, 
is about 42 degrees, while that 
made by the violet ray with the incident ray, or the angle S c q, is about 40 
degrees. It is in this way that the primary or principal rain-bow is formed 
by the united effect of innumerable rain-drops, each suffering two refrac- 
tions of light, and one reflection. 

627. There are often seen two bows, the one above the other, 
fainter, and with the colors in a reversed order. This is called 
the secondary rain-bow. The rays do not reach the eye of the 
spectator, until after two reflections and two refractions. 

Thus suppose the ray T r (see Fig. 253,) enters the drop B, at r, where 
it is refracted, at s it is reflected to t, and again reflected to u, where it is a 




626. Cause of the rain-bow. Explanation of the rain-bow. 

627. The secondary rain-bow. Cause of the arched appearance of the 
in-bow. 



2~0 



NATURAL PHILOSOPHY, 



Fig. 254. 



second time refracted, and passes on towards g. The red ray is still nearest 
the inverted ray T r, and the violet ray is the most distant. But a spectator 
at g would see the spectrum reversed in the secondary rain-bow. This is 
because the light enters at the lower part of the drop, and is transmitted 
through the upper part. The secondary bow is also fainter, in consequence 
of the light which is lost by two reflections. 

The arched appearance 
of the rain-bow is owing 
to the refracted rays being 
visible to our eyes, only at 
certain angles. Thus, if a 
line be drawn horizontal- 
ly, from the eye of the 
spectator, as E P, it is evi- 
dent that angles formed 
with this line of a certain 
dimension in every direc- 
tion, will pi-oduce a circle. 
Suppose three drops of rain 
only to be represented in 
the primary rain-bow, it 
will appear that the angle 
C E P is less than the angle 
B E P, and that the angle 
A E P is the greatest of the 
three. This larger angle 
is formed by the red rays, 
the middle one by the 
green, which is also the 
middle of the spectrum, and the smallest by the violet or extreme ray. 

628. Absorption of Light. The most transparent bodies in 
nature, as air and water, when in sufficient thickness, are capable 
of absorbing a great quantity of light. On the summits of high 
mountains, where light passes through a less thickness of atmos- 
phere, more stars are visible than in the plains below. On look- 
ing up through a considerable depth of water, luminous objects are 
scarcely visible. The red color of the morning and evening clouds 
is owing to the absorption of the colored rays by the air ; and the 
noon-day sun when viewed from a diving-bell, in the depths of the 
sea, appears of the same hue. It is supposed that the light ab- 
sorbed is stopped by the particles of the absorbing body, and re- 
mains within it, in the form of impenetrable matter.* All the light 
that is not either absorbed or transmitted is reflected, and the body 
assumes the color of the reflected ray. 

629. There is reason for believing that there are certain rays 
of solar light which never reach our globe. When a prism is very 

* Brewster's Optics. 




628. Effects of the absorption of light. Is the color of a body owing to 
light which is absorbed or reflected ? 

629. Black lines in the solar spectrum ; how accounted for? 



CONCLUDING REMARKS ON COLORS. 251 

perfect, and the sun-beam is received on a white sheet of paper, 
it presents the appearance of a ribbon shaded with all the prismatic 
colors, having its breadth irregularly striped by a number of black 
lines. These rayless lines are so narrow that they are scarcely 
visible without the aid of the microscope. But they are found 
always in the same part of the spectrum, and of the same propor- 
tional breadth. These vacant, or rayless lines in the solar spec- 
trum are supposed to indicate the existence of certain rays which 
do not come to us. It is imagined that they may be absorbed by 
the suns atmosphere. 

630. There are certain colored flames, which when examined 
by a prism, exhibit spectra deficient in particular rays, like the 
solar spectrum when examined by colored glasses. Pure hydrogen 
gas burns with a blue flame, in which many of the other rays are 
wanting. Alcohol when mixed with water, affords no other flame 
but yellow. Most of the salts, when exposed to the blaze of a 
lamp, give color to the flame as follows : 

Salts of soda — homogeneous yellow. 

" potash — pale violet. 

" lime — brick red. 

" strontia — bright crimson. 

" baryta — pale apple green. 

" copper — bluish green. 

631. Color is not an essential property of matter; but it arises 
from the action of matter upon light. Thus a white cloth reflects 
all the rays. But when dyed yellow, the particles of the cloth ac- 
quire the property of absorbing all the other rays, and of reflecting 
only the yellow. Bodies that reflect all the rays, appear white ; 
those that absorb all, appear black. Colored bodies decompose 
light by absorbing some of the rays and reflecting others. The 
color which a body seems to have, is, in reality, that for which it 
has no affinity, and therefore throws it off at its surface, while the 
other colored rays hide themselves among its particles. In the 
dark there is no color, for there is no light to be decomposed ; 
therefore, none to be absorbed and none reflected. So true is it, 
as expressed by the poet, that 

" Colors are but phantoms of the day, 

With that they're born, with that they fade away, 

Like beauty's charms, they but amuse the sight, 

Dark in themselves, till by reflection bright; 

With the sun's aid, to rival him they boast, 

But light withdraw, in their own shades are lost." 



630. Different colored flames. How produced. 

631. Color not an essential property of matter. Concluding remarks upon 



color 



PART VII. 

ELECTRICITY. MAGNETISM. 



LECTURE XXXVIII. 

THEORIES OF ELECTRICITY. MODE OF OBTAINING IT. 

CONDUCTORS AND NON-CONDUCTORS. 
ATMOSPHERIC ELECTRICITY. 

632. From considering the mechanical laws which govern 
solids, we proceed to the investigation of the laws of liquids, and 
next of air; then to the phenomena of sound as connected with 
air. We examined the properties of light, — that agent which, 
while it reveals to us other objects, is, itself, a mystery, confound- 
ing the wisdom of Philosophers, while it gratifies them by occa- 
sional discoveries of new and unexpected properties. We are now 
to contemplate another power in the machinery of the universe ; 
one, which, though long unknown to man, is around him on every 
side, and appears connected with almost all the physical changes 
which are taking place on the globe. This power is called elec- 
tricity, 

633. Electricity is, probably, a material substance. But such 
is its subtle nature, that few of the properties common to matter 
have yet been discovered as appertaining to it. Pervading the 
earth, its atmosphere, and all terrestial things, it neither afiects 
their temperature nor enlarges their volume. When undisturbed, 
it is quiet, giving no sensible tokens of its existence. But like the 
slumbering volcano, it is capable, when roused into action, of ex- 
hibiting a terrific force. 

634. Electricity was first observed as a property of amber, a 
resinous substance, called in Greek, electron, from whence the 

632. Retrospect of subjects considered. New subject. 

633. Is electricity known to be material ? 

634. Discovery of electricity. Electricity first ranked among the sciences. 



ELECTRICITY. 253 

name, electricity was derivod. Plato, and some other ancient 
writers, stated that amber, by rubbing, might be made to attract 
light substances, as the load-stone attracts iron. The same prop- 
erty of attraction had been observed in jet, emerald, and some 
other precious stones. But a few isolated facts and observations 
only, which seem to have excited little attention among the an- 
cients, were recorded by them. 

635. It was not until the last century that electricity took its 
rank among the sciences. Our distinguished countryman Dr. 
Franklin, is acknowledged as the author of some of the greatest 
discoveries concerning the nature of this fluid, and especially its 
identity with the lightning which flashes in the heavens. 

" To electricity," says Herschel, " the views of the physical inquirer now 
turn from almost every quarter, as to one of those universal powers, which 
nature seems to employ in her most important and secret operations. This 
wonderful agent, which we see in intense activity in lightning, and in a fee- 
bler and more diffused form traversing the upper regions of the atmosphere 
in the northern lights, is present probably in great abundance, in every form 
of matter which surrounds us, but becomes sensible only when disturbed by 
experiments of peculiar kinds. Every body is familiar with the crackling 
sparks which fly from a cat's back when rubbed. These by proper man- 
agement may be accumulated in bodies suitably disposed to receive them, 
and although then no longer visible, give evidence of their existence by a 
variety of extraordinary phenomena, — producing attractions and repulsions 
in bodies at a distance, admitting of being transferred from one body to 
another under the form of sparks and flashes ; traversing with perfect facility 
the substance of the densest bodies called conductors; producing painful 
shocks and convulsive motions, and if in sufficient quantity, even death itself 
in animals through which they pass; and, finally, imitating on a 6mall scale 
the effect of lightning." 

636. When we make use of the term electricity, or electric fluid, 
it must be understood that nothing more is implied than the un- 
known cause of electrical phenomena. 

Those who advocate the theory of a universal etherial fluid, which, by its 
vibrations causes the phenomena of light, very naturally consider electricity 
as intimately connected with that fluid ; and as light and heat both usually 
accompany electrical experiments, we have reason to believe that they all 
result from one source, but under different and complicated forms. Mag- 
netism and galvanism are known to be produced by electrical excitement; 
and to the same cause are referred some of the most important chemical 
changes. 

637. Explanation of Terms. Attraction is one of the most im- 
portant properties of electricity. On rubbing a glass tube with a 
dry silken handkerchief, it attracts light bodies, as down, silk, cot- 
ton, &c. When a body exhibits electrical appearances, it is said 
to be excited. A body receiving electricity is said to be electrified. 
An electrified body is said to be insulated, when it is so situated 
that its electricity cannot escape. Conductors are substances 

635. General characteristics of electricity. 

636. What is understood by the term electricity? 

22 



254 NATURAL PHILOSOPHY. 

which readily transmit the electric fluid ; non-conductors prevent 
its free passage. Glass and amber are both capable of electrical 
excitement ; but the electricity of the one, presents different prop- 
erties from that of the other. The same difference is observed 
with respect to various other substances. The term vitreous is 
applied to that electricity which appears on exciting glass and other 
•analogous bodies, and the term resinous to that which appears in 
amber, sealing-wax, and other resinous substances. The term 
positive when applied to electricity is synonimous with vitreous, 
and negative with resinous. 

638. Theories of Dr. Franklin and Du Fay. Dr. Franklin's 
theory of electricity supposes that there is one electric fluid which 
exists in all bodies, and is naturally in a state of rest. That when 
the equilibrium is destroyed by friction or any other exciting cause, 
one body becomes plus, or positively electrified, while the body 
in contact becomes minus, or negatively electrified. Thus when 
a glass tube is rubbed with a piece of silk, the tube gains and the 
silk loses electricity. 

A theory of a different kind, which was advanced in France, by 
Du Fay, previous to the time of Franklin's discoveries, is now 
strongly advocated. This theory supposes the existence of two 
antagonist electric fluids, called the vitreous and the resinous, (from 
glass and resin, the two substances from which they are respect- 
ively produced,) which like an acid and an alkali neutralize each 
other. It is only when separated, that they manifest their peculiar 
properties, and the most striking appearances are exhibited at the 
instant in which they unite. As either of these theories satisfac- 
torily explain most of the electrical phenomena, it is not necessary 
to enter into a consideration of their comparative merits. The 
theory of Franklin has the advantage of simplicity. According to 
the analogies of nature we should not be inclined to attribute to 
two agents that which could be effected by one ; and by an 
acknowledged rule in philosophy, no more causes should be as- 
cribed than are necessary to account for the phenomena. Some, 
indeed, assert that there are phenomena accompanying the trans- 
fers of electricity from body to body, and the state of equilibrium 
it affects under various circumstances, which appear to require the 
admission of two distinct fluids, antagonist to each other, each at- 



637. Attraction. Electrical excitement. An electric body. Conductors 
and non-conductors, Electricity of glass and of amber. Vitreous and resi- 
nous electricity. Positive and negative electricity. 

638. Franklin's theory of electricity. Theory which originated in France. 
The student not obliged to adopt or reject either theory. Why is Franklin's 
theory the more simple? Positive and negative fluids distinguished from 
positive arsd negative electricity. 



MODE OF PRODUCING ELECTRICITY. 255 

trading to the other, and repelling itself. The terms positive and 
negative fluids are sometimes used by the advocates of two fluids, 
and must be distinguished from positive and negative electricity, 
which refer to the different states of the same fluid. 

639. Exp. 1. Rub a piece of sealing-wax with silk, fur, or 
flannel, and it will have acquired the power of attracting sub- 
stances. If a small pith ball be suspended by a silken thread, a 
feather or bit of cotton will be alternately attracted and repelled 
by the excited body. 

Exp. 2. If a glass tube be rubbed several times in the dark, 
and the finger be brought within half an inch of it, a spark will 
be seen between the finger and tube, accompanied by a snapping 
noise, and a sensation like the prick of a pin. 

These experiments prove that electricity is excited by friction, 
and that attraction, repulsion, light and sound are electrical phe- 
nomena. 

640. The presence of electricity, its nature and quantity may be 
determined by a very simple instrument called an electrometer. 
The pendulum electrometer consists of a glass rod fixed to a stand, 
and bent at the top. A thread of silk, with a very small pith ball 

attached, is suspended from the glass hook. By 
Fiff. 255. means of this little instrument, it is easy to determine 
whether the electricity given off by any substance, 
be vitreous or resinous. When the pith ball of the 
electrometer is excited by glass, it will be repulsed 
by any body having the vitreous electricity ; and at- 
tracted by any body having the resinous electricity. 
On the contrary, if the pith ball of the electrometer 
be excited by sealing-wax, it will be repelled by the 
resinous and attracted by the vitreous electricity. 

641. The two kinds of electricity are produced at 
the same time, the one kind in the body rubbed, and 
the other in the rubber. When a glass tube is rub- 
bed with silk or flannel, as much positive electricity 
is excited in the glass, as there is negative in the silk. The kind 
of electricity depends on the substance rubbed. If dry flannel be 
rubbed against smooth glass, the flannel acquires the resinous, and 
the glass the vitreous electricity. When two plates of glass, one 
polished and the other rough, are rubbed against each other, the 
polished surface has the positive, and the rough surface the nega- 
tive electricity. 

639. Exp. 1. Exp. 2. 

640. Nature and use of the electrometer. 

641. Effects upon the body rubbed and the rubber. On what does the 
kind of electricity depend ? 



a 



256 NATURAL PHILOSOPHY. 

642. The following substances become positively electrified if 
rubbed with either of those mentioned after them, and on the con- 
trary, they become negatively electrified when rubbed with either 
of those named before them. 

1. Fur of a cat, 6. Paper, 

2. Polished glass, 7. Silk, 

3. Wool and flannel, 8. Sealing-wax, 

4. Feathers, 9. Rough glass, 

10. Sulphur. 

The fur of a cat, when rubbed against any of the bodies above 
named, affords the vitreous (positive) electricity. Sulphur, when 
rubbed against any of the bodies above named, affords the resinous 
(negative) electricity. Silk becomes negative when rubbed 
against paper, feathers, &c, but positive when rubbed against 
sealing-wax, rough glass, or sulphur. Thus when silk stockings 
have been worn over woolen, sparks and a crackling noise are 
often perceived on separating them. 

Conductors and Non-conductors of Electricity. There is a 
great difference in the power of bodies to conduct or transmit the 
electric fluid. Among the conductors are the metals, charcoal, 
living animals, jlame^ smoke, steam and damp air. Among the 
non-conductors are resins, sulphur, wax, glass, silk, wool, hair, 
feathers, &c. The air when dry is a non-conductor, as are all 
vitreous and resinous substances. 

643. Bodies surrounded with non-conductors are said to be in- 
sulated, because when excited, their electricity cannot escape. 
But when they are not insulated, the electricity is conveyed to the 
earth, which is a conductor. In order to accumulate electricity, 
therefore, the excited substance must be insulated. If the air, as 
well as the earth, were a conductor, it would be very difficult to 
accumulate electricity. Damp air being a conductor, it is quite 
necessary to the success of the experiments on electricity, that they 
be performed in dry weather, unless the air of the room be dried 
by artificial heat. 

644. Electrical Apparatus. The electric machine is used in 
order to accumulate large portions of electricity, for the purpose of 
experiment. 

Fig. 256, represents what is termed a plate machine. This 
consists of a circular glass plate A, nearly two feet in diameter, 
turning upon an axis which passes through its center. The plate 
is rubbed by two pairs of cushions B B. C, called the prime con- 

642. Substances remarkable as conductors or non-conductors of electri- 
city. 

643. An insuliit.ed body. 

6'44. Describe the electrical machine. 



ELECTRICAL APPAKATU.5. 



257 



Fig. 256. 




ductor, is a brass cylinder having 
two branches, so as to receive 
electricity from each cushion. 
E E are pieces of oiled silk pass- 
ing from the cushions near to the 
points of the conductor. F is the 
handle by which the plate is turn- 
ed. The cushions are stuffed 
with hair and coated with an 
amalgam composed of tin, zinc 
and mercury, a substance which 
has been found to cause a great 
degree of electrical excitement 
when rubbed against glass. When 
the glass plate is made to re- 
volve rapidly, if the machine is 
properly prepared and the atmos- 
phere in a dry state, shocks will be 
felt and vivid flashes of light seen 
passing over the surface of the glass, and from the cushions to the 
conductor. The light is supposed to be occasioned by the sudden 
compression of the air, owing to the escape of the electric fluid. 
Heat is also evolved, for gun-powder, alcohol and other inflamma- 
ble bodies are set on fire by the electric spark.* 

645. The principles on which the electrical machine operates, 
are the following : 1. The rubber communicates with the floor by 
means of a metallic chain, which is a conductor of electricity ; 2. 
The floor communicates with the earth, from whence are derived 
inexhaustible stores of the electric fluid ; 3. By the friction of the 
glass, positive electricity is acquired by the rubber, and this is 
attracted and carried off' by the metallic points of the prime con- 
ductors, in which it becomes accumulated. On presenting the 
knuckle to the conductor, a spark is seen, and a peculiar prickling 
sensation is felt. There is no greater mystery in this than there 
is in the pain we feel on touching a hot iron. In the latter case, 
it is the passage of caloric into the hand which causes the sensa- 
tion ; in the former case, it is the passage of electricity ; and we 
know no more what caloric actually is, than we do what electricity 
is, considered in relation to its essence. 



* For a description of the Cylinder Machine, see the author's Chemistry 
for Beginners, page 73. 



645. Principles on which the electrical machine operates. Cause of the 
sensation produced by electricity. Suppose the rubber to have no commu- 
nication with the earth. 

22* 



258 



NATURAL PHILOSOPHY. 



Fig. 257. 



If the communication between the earth and the rubber be cut 
off, the supply of electricity to the machine would soon be ex- 
hausted. 

646. The passage of electricity from one substance to another 
is termed induction. Active electricity, existing in any substance, 
tends always to induce the opposite electrical state in the bodies 
t^iat are near it. 

647. By various experiments it has been found that electricity 
remains at, or near, the surface of bodies. It is found that in con- 
ductors of an elongated figure, the electric fluid is accumulated to- 
wards the two ends, and withdrawn more from the central parts. 
Thus it is that electrical conductors. terminating in a conical point, 
part with their electricity so readily. 

648. When the electric fluid is 
to be collected in large quantities for 
the purpose of experiments, a ves- 
sel, A, called the Leyden jar* is 
made use of. It consists of a thin 
glass jar, coated internally and ex- 
ternally, to within about two inches 
of its mouth, with tin foil. The ac- 
cumulation of the fluid in this jar is 
called "the charge:" this is effected 
by connecting the brass wire with 
the knob at its top, with the conduc- 
tor of the machine. On working 
the electrical machine, the fluid is- 
sues from it to the jar, rendering the inside positively, and the out- 
side negatively electrified. 

649. This charge would remain for a short time, but would be 
gradually dissipated by the action of the air. But when the charge 
is to be passed through any substance, the discharging rod B is 
used. By applying one of the ends to the outside of the jar, and 
bringing the other towards the knob communicating with the inside, 
an explosion takes place, and the equilibrium between the inside and 
the outside of the jar is restored. The charge of a jar which would 
contain a gallon, is quite sufficient to fire gun-powder, or any other 
inflammable substance. A single spark will kindle spirits of wine 

* So named from Leyden, in Holland, the place where it was first con- 
structed. 




646. Induction. 

647. Why conductors are of an elongated conical figure. 

648. Explain the construction of the Leyden jar, with the manner in which 
it is charged. 

649. Use of the discharging rod. Electrical battery. 



ELECTRICAL APPARATUS. 



259 



Fig. 25b. 




Fig. 259 



or ether; buf when 
great intensity is re- 
quired, such as is suf- 
ficient to fuse steel 
wire, deflagrate gold, 
or silver-leaf, &c, a 
combination of jars, 
which may be all dis- 
charged at the same 
instant, is required. 
This combination is 
called the electrical 
battery, and is usually 
constructed as in the 
figure. 



1 



650. An instrument called the spiral tube serves to ren- 
der the course of the electric matter visible, and shows its 
color in a beautiful manner. One end of it is applied to 
the ball of the conductor, the other end being held in the 
hand ; the spark from the conductor instantly passes from 
one spangle of the tin foil, on the glass tube, to the other, 
and brilliantly illuminates the whole. This experiment 
may be varied at the will of the operator; and drawings 
or sketches of any kind may be laid down on plates of 
glass, and thus rendered luminous. 

651. The electrophorus is a simple Fig. 260. 
machine, consisting of an under plate 
or sole, B, covered with a resinous 
coat, and an upper plate or cover, A, 
of metal or wood coated with tin-foil, 
and having a handle I, of glass, or 
some non-conducting substance. The 
resinous plate, being rubbed with a 
piece of fur, becomes charged with 

negative, or resinous electricity. The upper plate A, is now 
placed upon the sole, or resinous plate, and the finger being ap- 
plied to the former, receives electricity, which may be transferred 
to a Leyden jar, by touching the knob. After repeating this pro- 
cess several times, the jar may be found sufficiently charged to 
cause a loud report, on the application of the discharging rod, and 



I 




650. Spiral tube. 

651. Electrophorus; and the mariner in which electricity may be accu- 
mulated with it. Is the charge in the Leyden jar, of the same kind of elec- 
ricity 1 



263 



NATURAL PHILOSOPHY. 




to set fire to cotton. Although the negative or resinous electricity- 
is first excited by rubbing the under plate with the fur, the charge 
in the Leyden jar is of the opposite kind, viz., the positive or vit- 
reous. The fluid which is obtained by induction being always 'lie 
opposite of that of the excited body. Thus, if instead of a plate 
coated with resin, a glass plate be used, the negative or resinous 
electricity will be obtained. 

652. Electrical bells. The figure repre- 
sents four bells, abed., hanging by brass 
rods, with a bell fixed on a brass pedestal, 
A B, and four small brass balls suspended by 
silken threads. The brass rods which sus- 
tain the four balls, being connected with the 
prime conductor of the electrical machine, 
becoming electrified, attract the brass balls 
which hang by silk, and these acting as clap- 
pers cause a ringing ; the balls having gain- 
ed electricity by this contact with the bells, 
fly off, and are attracted towards the middle 
bell where they discbarge themselves. 

They are now ready to be attracted again by the bells, which are 
continually receiving new portions of electricity from the elec- 
trical machine ; and thus the ringing of the bells may be contin- 
ued as long as the machine is in operation. 

653. An insulating stool is a small foot- 
stool with glass feet. A person standing on 
this stool is said to be insulated, that is, 
there is no medium by which electricity can 
be conducted from him. If a person thus in- 
sulated, hold in his hand a chain connected 
with the prime conductor, his body will 
become a conductor, giving off electrical 
sparks to substances presented to it, and at- 
tracting such as are sufficiently light ; his hair, which is similarly 
electrified, will rise and diverge in all directions, each single hair 
mutually repelling and being repelled by the others. 

654. Dancing figures illustrate, in an amusing manner, some of 
the properties of electricity, particularly that of attraction and re- 
pulsion. Two metallic plates are represented in the cut. The 
lower one is connected with the floor. The upper plate being 
electrified by a communication with the prime conductor, at- 
tracts towards it light bodies. Let small figures, cut from some 
light material, such as pith, paper, or the like, be placed on 

652. Electrical bells. 

653. Insulating stool. 

654. Dancing figures. 



Fig. 262. 




ELECTKICAL Al'l'ARATUS. 



261 




Fig. 263. the lower plate ; on suspending the upper plate 

at a little distance above them, they are at- 
tracted towards it. When the figures touch 
the electrified plate they acquire electricity, 
and are, of course, repelled by the upper, 
and attracted by the lower plate, now in an 
opposite electrical state. Discharging them- 
selves by contact with the lower plate, they 
are again negative, and in a condition to be 
attracted by the positive plate suspended over 
them. Thus the electrified figures are alter- 
nately attracted and repelled by each other, 
as they are in opposite or similar states of 
electricity : and a very lively dance among the little excited im- 
ages, is thus kept up as loug as the upper plate continues to re- 
ceive electricity. 

655. The li^ht from the electric spark appears as a pencil of 
rays or as a star, according to the species of electric fluid which 
causes it. A Leyden jar being charged with positive or vitreous 
electricity, its outside coating is negative, or has the resinous elec- 
tricity. Let the discharging rod, having its ends pointed, be pre- 
sented, so that one of its points shall 
be within an inch of the knob of the 
jar A, and let the other point be as 
near to the outside coating of the jar ; 
the point C will be illuminated with 
a star, and the point B with a pencil 
of light. This is because the electric 
fluid, going from the inside to the out- 
side of the jar, (or making the elec- 
tric circuit) enters at the point C, and 
issues from the point B. But if the 
jar is electrified negatively on the in- 
side, the outside will then be posi- 
tive, and the electric fluid will pass from the outside to the inside 
of the jar ; the pencil of rays will then appear on the point C, and 
the star on the point B. The positive or vitreous electricity is 
therefore designated by the pencil of rays which indicate the pas- 
sage of the fluid from the conductor, and the negative or resinous 
electricity by the star which shows the fluid entering the conductor. 

656. The effect of electricity upon animals is so remarkable 
that it is not strange, that when first discovered, it should have 




655. Light from the electric spark varies according to the species of elec- 
tricity. 

656. Effect of electricity upon animals. 



262 NATURAL PHILOSOPHY. 

excited great attention, and many extravagant notions with respect 
to it should have prevailed. Men who had acquired some practical 
knowledge of electrical apparatus, but were ignorant of philosophical 
principles, travelled about, astonishing the credulous, and deluding 
the sick, lame, and impotent with the fallacious hope that by sub- 
mitting to the process of " electerizing" that is, to receive a shock 
from a charged jar, they would obtain a certain cure for all their 
diseases. 

657. The animal system is a good conductor of electricity. If 
any number of persons join their hands, and the first in the circle 
presents a discharging rod to the outside coating of a charged 
Leyden jar, at the same time the last in the series touches with 
another rod, the knob of the jar, thus forming an electric circle, a 
shock is felt throughout the whole circle, and by every one in it at 
the same instant. If the jar is charged with positive electricity, 
the fluid will issue forth from the knob of the jar, and run through 
the circle till it is discharged through the person who touches the 
outside coating of the jar ; but if the outside coating is positive, the 
fluid will pass in a contrary direction. 

So rapid is the motion of electricity, that it seems to be instan- 
taneous ; but like light it is doubtless progressive, though its ve- 
locity is inconceivably great. 

Atmospheric Electricity. 

658. There is always more or less electricity in the atmosphere. 
This may be ascertained by experiments with a simple apparatus 
called the electrical kite. This has for a conductor, a fine metal- 
lic wire twisted with the cord which forms the string. This con- 
ductor is insulated by being attached to a silken string. When 
this kite is raised in the atmosphere, the presence of electricity is 
manifested by an electrometer connected with the lower end of the 
conductor. When the electricity of the atmosphere is excited, as 
manifested by thunder clouds, there is much danger in thus draw- 
ing down the lightning. 

659. The electricity drawn from the clouds by the electrical kite, or a 
conducting rod, may be accumulated in a Leyden jar; and its properties are 
found to be the same, as those of the fluid produced by the electrical ma- 
chine. Doctor Franklin observing various electrical phenomena, was led, 
by reasoning from analogy, to believe lightning an effect of the same cause. 
This theory he proved by experiments made with an electrical kite during 
a thunder storm. The following are some of the resemblances pointed out 
by this Philosopher, between electricity and lightning. 



657. Electric circle. Motion of electricity. 

658. Electrical kite. 

659. Nature of atmospheric electricity. 



ATMOSPHERIC ELECTRICITY. 



203 



660. 1. The zigzag form oflightning corresponds exactly, in appearance, 
with a powerful electric spark passing through a considerable interval of air. 

2. Lightning most frequently strikes high bodies, as the summits of hills, 
high trees, towers, spires, chimneys, &c. So the electric fluid, when puss 
ing from one body to another, always seizes on the most prominent parts. 

3. Lightning and electric matter are both found to pass most readily through 
those substances that are good conductors, such as metals, water, &c, and 
to avoid those that are non-conductors, as glass, silk, sealing-wax, resins, &c. 

4. Lightning inflames combustible bodies ; the same is readily effected by 
electricity. 5. Metals are melted by a powerful charge of electricity ; this 
is one of the most common effects of a stroke of lightning. 6. Lightning 
fractures and disperses all brittle substances ; the same holds true with re- 
spect to the electric fluid. 7. Lightning often produces blindness ; the same 
effect is found to be produced on animals when subjected to a strong elec- 
tric charge. 8. Animal life is destroyed by lightning; strong discharges 
of the electric fluid will produce the same effect. 9. The magnetic needle 
is similarly affected by lightning and electricity, and iron may be rendered 
magnetic by both causes. 

661. The charging and discharging of electrics is a miniature representa- 
tion of the sublime process which is going on in the heavens during a thun- 
der storm. Thus a cloud positively electrified, will draw towards it, clouds 
that are negatively electrified ; when these clouds approach within what is 
termed their striking distance, the fluid darts from the positive to -the nega- 
tive cloud ; the explosion produces a loud report, which being echoed from 
cloud to cloud, produces the rolling noise called thunder. It frequently 
happens that the lightning during a thunder storm is seen darting from the 
clouds towards the earth, and there producing dreadful effects. This may 
be caused by the earth, over which the storm happens, being, at the time, 
negatively electrified. The letter a represents a portion of the earth's sur- 
face ; c, the lower or non- 
conducting part of the at- 
mosphere, d d, the clouds 
charged with electricity ; 
g g, the positive electricity 
of the clouds, met by the 
negative electricity q q, of 
the earth ; n n, the points 
where the two electrici- 
ties meet, and where the 
explosion takes place. — 
This explosion is often 
very terrible, accompanied 
with intense lightning and 
astounding thunder, and 
rending in sunder every- 
thing in its way. Build- 
ings that are lofty are much exposed to its effects ; and hence the necessity 
of having metallic cunducting-rods raised on them. Green trees being good 
conductors of electricity, those which rise high into the atmosphere often 
attract the fluid towards them ; it is, therefore, highly dangerous to go under 
them for shelter during a thunder storm. It is safer to remain in the open 
air at the distance of about forty or fifty feet from trees or houses. Within 



Fig. 265. 




660. Analogies between lightning and electricity. 

661. Discharge of electricity from the clouds. Conducting-rods. Danger 



264 



NATUltAL PHILOSOPHY. 



Fig. 266. 



doors, the middle of the room should be preferred, and such a position might 
be rendered still more safe, by standing on a glass-legged stool, or hair mat- 
tress, or even a thick woollen hearth-rug. In a thunder storm the middle 
story of a house is considered the most secure, and the cellar the most ex- 
posed part of it. 

662. Thunder is supposed to be caused by the motion of the air 
rushing in to fill the void made by the sudden passage of the elec- 
tric fluid. Lightning is supposed to be caused by the sudden con- 
densation of the air, produced by the compressed force of the elec- 
tric fluid.* The lightning is seen before the thunder is heard, 
because light travels faster than sound. 

Aurora Borealis. 

663. It is now generally believed, that the beautiful meteor, cal- 
led the Aurora Borealis, or northern lights, is occasioned by the 
passage of electricity through the upper regions of the atmosphere, 
where the air is some thousand times more rarefied than at the 
earth's surface. 

The figure represents a large glass tube fitted with a brass cap 
at the top, from which projects into the tube a wire terminating 
in a ball. At the lower end of the tube, projects a similar wire, 
but pointed at the extremity. This tube, being exhausted by 
means of an air-pump, on applying the electrical machine, the 
electrical fluid will pass between the two wires, in a diffused 
luminous stream, having all the characteristic appearances of the 
northern lights. There is the same variety of color and intensity 
within, the same undulating motion and occasional coruscations ; 
the streams exhibit the same diversity of character, at one mo- 
ment minutely divided in ramifications, and at another beaming 
forth in one body of light, or passing in distinct broad flashes. 

664. The cause of the aurora borealis was long un- 
known. At present, Philosophers agree in referring it 
to electrical agency. It appears generally in the form 
of a luminous arch above the northern horizon, and 
extending from east to west across the heavens ; but 
never from north to south. Those who witness the 
peculiarly soft, and brilliant light produced by electricity in passing 
through a tube of highly rarefied air, cannot but be struck by its re- 
semblance to the beautiful illumination of the aurora borealis, and 
will readily believe them to be effects of the same cause.*)" 

* In this case, it is supposed caloric is brought from a latent state in the 
atmosphere to a free state, in which it is accompanied by light. 

t At about nine o'clock on the evening of January 25, 1837, at Brattlebo- 
rough, Vermont, while the author was engaged in preparing this work, she 



662. Cause of thunder and lightning. 

663. Aurora borealis, its connection with electricity. Experiment to show 
the effect of electricity upon rarefied air. 

664. Supposed cause of the aurora borealis. 



MAGNETISM. 265 

665. Though the name Northern Lights has been given to this 
phenomenon, the same luminous appearances are occasionally ex- 
hibited in the southern hemisphere. As such sublime displays of 
created effulgence are never made in vain, these polar accumulations 
of the electric fluid doubtless subserve some wise and conservative 
principle in the economy of nature. May it not be that, by this 
means, an electric circuit is formed between the equator and the 
poles, and the equilibrium in the earth's electricity thus main- 
tained ?* 



LECTURE XXXIX. 

MAGNETISM. DIP OF THE MAGNET. DEVIATION OF THE COMPASS. 

THEORY OF MAGNETISM. THE COMPASS. 

666. Magnetism is the science which treats of the properties and effects of 
the magnet. Accustomed as we are to examine things by our external 
senses, it requires some faith to believe in the existence of matter which is 
not manifest to one of these senses. The electric fluid, though neither tan- 
gible, nor visible, in its effects, is seen, heard and felt. Magnetism is a 
silent, invisible and intangible agent; but we see its operations, and there- 
fore we give credence to philosophers who assure us that these effects must 
proceed from some cause, the name of which they call magnetism or the 
magnetic fluid. Would it not be very inconsistent, should these philoso- 
phers attempt to overthrow the christian's faith in the existence of God, on 
the ground that he has no sensible evidence of such a being? A bar of iron 
attracts towards it a small bit of steel; — this, the philosopher says, is caused 
by the power of magnetism. Must so simple an effect be the result of a 
cause, and, yet, the universe, itself exist uncaused ? Shall this regularity, or- 
der, and harmony of the creation be ascribed to accident, chance, or nothing, 
because the philosopher has never seen the Power which created and up- 
holds all things; — because the power is not embodied and directly revealed, 
in all its ineffable magnificence, to the bodily sense of man 1 This argument 
may, to some, appear unconnected with the subject of our present lecture, 
but philosophy and religion have been too long viewed as entirely distinct, 

was called to witness one of the most splendid exhibitions of this phenome- 
non, which has ever been seen in our latitude. It can scarcely be expected 
that any persons now living will ever again see so sublime a display of 
Almighty power in a similar form. 

* Chemical Electricity is treated of in the Author's larger work on Chem- 
istry. 

665. Northern lights not confined to the northern hemisphere. Sugges- 
tion with respect to this phenomenon. 

666. Definition of magnetism. Reflections suggested by the subject of 
magnetism. Religion and philosophy not entirely distinct. 

23 



266 NATURAL PHILOSOPHY. 

if not at variance with each other. The young need to have their faith in 
an unseen, superintending providence, strengthened by various considera- 
tions ; and when, in the course of their scientific pursuits, arguments leading 
to this end present themselves, it is not to be counted as time lost if they 
pause to reflect upon them. 

667. We admit the existence of an unknown cause of certain 
phenomena called magnetism, and the bodies in which this unknown 
cause operates are called magnets. 

The phenomena of magnetism are, 1st. attraction and repulsion; 
2d. the power of the magnet to impart its properties to other masses 
of steel or iron ; and 3d. its tendency to point towards the poles of 
the earth. 

668. A magnet may be either natural or artificial. The natu- 
ral magnet is an oxide of iron, of a dark grey color, very heavy, 
and with a metallic lustre. It has long been known as the load- 
stone. It is usually found in beds of iron ore, in irregular masses 
of a few inches in diameter ; but, sometimes, in larger quantities. 
There are natural magnets of more than one hundred pounds 
weight, with the power of lifting two hundred pounds of iron by 
means of their attractive property. Every magnet has two op- 
posite points called poles ; and at 

Fig. 267. these points, the attractive power 

^ ^ ^.,/ :,;:^ i s greatest. The poles are called 

f^^^Sig gp =s the north and south poles, (see N 

r - ^FF«^ -^5^ I" and S in the figure) accordingly as 

they point to the north or south 
pole of the earth. The imaginary straight line, N S, which joins 
the poles, is called the axis. If a magnet be immersed in iron 
filings, they will attach themselves to it until it is completely covered. 
At the poles of the magnet, the attracted filings will stand erect (as 
at Fig. 267 ;) but they gradually become less perpendicular, till, 
in the center, they lie in a horizontal position. The curves thus 
formed, are called magnetic curves. 

669. The magnetic power like electri- 
Fig. 268. city, may be transmitted from one body to 

another. Thus by rubbing bars of iron or 
steel* with a magnet, an artificial magnet 
is formed, possessing all the properties of 
the natural one. Suppose a magnetized 
steel needle to be exactly balanced upon a 
pivot, like that of the mariner's compass, 

* Steel is the carburet of iron, or iron combined with carbon. 




667. Magnets. Phenomena of magnetism. 

668. Loadstone. Where found. Poles of the magnet. Iron filings at- 
tracted by a magnet. Magnetic curves. 

669. Transmission of the magnetic power. Artificial magnet. Polarity. 



DIP OF THE MAGNET. 2G7 

so that it can move freely towards any point, it will not rest until 
its poles point nearly north and south. If this position is changed, 
the needle will vibrate until it settles in the same line as before. 
This is called the polarity, or directive property of the magnet. 

Dip or Inclination of the Magnet. 

670. The two poles of the magnet, when at liberty to move 
freely, do not lie exactly in a horizontal direction, but one pole in- 
clines a little downwards, thus proportionally elevating the other 
pole. This is called the inclination or dip of the magnet. Ingo- 
ing north, the north pole of the magnet is depressed ; and the near- 
er the pole, the greater the depression. It is supposed that if the 
needle could be carried to the pole it would assume nearly a ver- 
tical position, its northern pole pointing perpendicularly down- 
wards, and its southern pole upwards. 

Suppose N S to be a magnetic bar whose north pole is N, and whose south 
pole is S ; if a magnetic needle turning on a point were presented to the 
magnetic bar, it would assume the various positions of the arrow in 
Fiff. 269. ^S- 269, n and * re- 

presenting the north 
and south poles of the 
needle, and c the pivot 
on which it turns. It 
will be seen, that the 
south pole of the nee 
die points directly to 
the north, and the 
north pole of the nee 
* d die to the south pole 

of the magnet ; as the needle is moved from either pole towards the center 
of the magnet, the dip becomes less and less, until at the center it is hori 
zontal. If the earth itself were a vast magnet, having its poles at some dis 
tance below the surface, the magnetic needle would show precisely the 
same dip that it does now. It was formerly believed that magnetic attrac- 
tion below the earth's surface produced this phenomenon ; but late observa- . 
tions, by showing the existence of circulating currents of electricity around 
the earth, have led to the opinion that this is the cause of the earth's appa- 
rent magnetism. If this hypothesis be true, it is attraction from above, and 
not from below, that causes the dip of the poles of the magnetic needle. 
There are reasons to believe that the phenomena of magnetism are caused 
by opposite electricities ; in which case the poles of the magnetic bar and 
needle are attracted by antagonist electrical fluids. 

Fig. 270. 671. That line around the earth 

where the magnetic needle has no 
dip, or maintains a horizontal posi- 
tion, is called the magnetic equator. 
This does not coincide directly with 
the earth's equator, E E, but may be 

670. What is meant by the dip of the magnet ? How is the subject illus 
trated ? 

671. Magnetic equator. 





269 



NATURAL PHILOSOPHY. 



Fig. 271. 



considered as a great circle surrounding the earth, and in- 
clined to its equator, at an angle of about 12 degrees. It crosses 
the equator at several different points. This line is represented 
by the letters M M M. 

Deviation or Declination of the Compass. 

672. The magnetic needle moving freely, does not point di- 
rectly to the poles of the earth ; this variation is called by mari- 
ners the declination or deviation of the compass. Although the 
deviation of the magnetic needle was known to some philoso- 
phers, two hundred years before the time of Columbus, yet it was 
not generally understood by mariners. For when the crew of that 
navigator, on his first voyage of discovery, learned that the needle 
of their compass did not point directly to the pole, they were alarm- 
ed, and losing all confidence in that only sure guide to the mari- 
ner, grew more mutinous towards their commander, through fear 
that he would never be able to conduct them back to their homes. 

Due allowance being made for the variation of 
the magnetic needle, the exact points of the com- 
pass maybe ascertained. Thus suppose the line 
N S to represent the true meridian, or a line drawn 
due north and south, and that which is drawn at 
right angles represents the equator, or a line from 
east to west. The magnetic needle does not fall 
on the meridian, as it would do if it pointed directly 
to the north pole, but deviates from it, making the 
angle BON, the line B being 15 degrees north. 
This shows the declination or deviation of the 
needle ; when this deviation is towards the west, 
as seen at B, the declination is said to be 15 degrees 
westerly. 

673. By the magnetic meridian is meant a vertical circle in the heavens, 
supposed to be drawn through a line in which the needle naturally places 
itself. This meridian does not, as we have seen, always correspond to the 
geographical meridian, though there are places in which the magnetic nee- 
dle, freely suspended, points directly to the poles of the earth, in which case 
the meridians coincide. Lines drawn on the globe through all places where 
the magnetic and geographical meridians coincide, or where the needle 
points due north and south, are called lines of no variation. But such lines 
are themselves variable ; as the direction of the needle is not constant in the 
same place, but is subject to change, through the influence of some unknown 
cause. 

In 1657, according to observations then made in London, there was no 
variation, the needle pointing directly to the north pole of the earth, and 
consequently coinciding entirely with the earth's meridian. After this pe- 
riod it began to vary a little towards the west. This variation continued 




672. What is meant by the deviation of the compass ? Method of calcu- 
lating the variation of the needle. 

673. Magnetic meridian. Lines of no variation changing place, 
netic poles of the earth. 



Mag- 



THEORY OF MAGNETISM. 269 

progressively until 1818, when the angle of declination was 24° 30 minutes 
west. Since then, it lias been slowly inclining towards the east. This de- 
viation of the compass to die eastward and westward, seems to resemble the 
oscillations of a pendulum, which moving slowly over an arc of many de- 
grees of the earth's surface, should require some hundred years to go from 
one extremity of the arc to the other. 

To account for the phenomenon of the declination of the compass, 
it has been supposed that there are magnetic poles constantly re- 
volving, and that these poles do not coincide with the poles of the 
earth, except at very long intervals. Late observations have ren- 
dered it probable that there are magnetic poles in each hemis- 
phere. One has been discovered in Siberia ; and Ross and Par- 
ry, in their late reports of discoveries in the polar seas, state that 
there is also an American magnetic pole, about 180 degress dis- 
tant from that on the eastern continent. 

Theory of Magnetism, 

674. In observing the phenomena of magnetism we see no 
agent, we hear nothing to inform us of its action, and we can feel 
or touch nothing which gives evidence of its existence. But we 
perceive the effects of the agent called magnetism. When we see 
tilings of iron, or a steel needle moving towards a bar of iron, nei- 
ther impelled nor drawn by any perceivable external force, and 
adhering with tenacity after they have come into contact, we per- 
ceive something for which we cannot account, otherwise than by 
referring it to a power called magnetism residing in the iron. We 
are more struck with this phenonemon, than with the attraction of 
gravitation, because it is less common ; and yet it is no more won- 
derful that the needle should move towards the iron bar, than that 
the apple when loosed from the bough, should move towards the 
earth. But while the attraction of gravitation is an universal prin- 
ciple, that of magnetism is confined to a very few substances, 
chiefly to iron and steel, and this limitation renders its operations 
still more mysterious. 

675. But though magnetism works in silence and obscurity, while elec- 
tricity is attended by the flash, the thunder, and the shock, we have reason 
to believe they are but different modes of operation of one, and the same 
agent. 

1st. Magnetism and electricity, alike consist of two species ; the northern 
and soitthern* polarities, and the positive and negative electricities. 

* Called also boreal (northern) and austral (southern) magnetism. 

674. Magnetism known only by its effects. 

675. Reasons for believing that magnetism and electricity are the same 
agent. 1st. With regard to the two species. 2d. Similarity of laws. 3d. 
Effect of combination. 4th. Diminution of force according to the square of 
the distance. 5th. Communicated by induction. 6th. Two theories of mag- 
netism corresponding to the theories of electricity. 

23* 



270 NATURAL PHILOSOPHY. 

2d. They are governed by the same laws, viz., that similar powers repel, 
and dissimilar powers attract each other. 

3d. The magnetic influence is destroyed by the combination of the two 
polarities, and the electric action ceases on the union of opposite electri- 
cities. 

4th. The force, both of magnetism and electricity, varies, inversely, as 
the squares of the distance. By comparing the number of vibrations of a 
magnetized needle, during the same time, at different distances from the 
magnet, it is found that the magnetic intensity, like every known force pro- 
ceeding from a center, diminishes with the distance ; and, as in the attraction 
of gravitation, diminishes in an inverse ratio of the square to the distance. 
A magnetic needle, being, carried out of the direction in which it naturally 
rests, and left free again, vibrates in a manner similar to the vibrations or 
oscillations of a pendulum, until it has returned to its natural position. The 
greater the magnetic intensity which influences the needle, the greater will 
be the velocity of its vibrations, as the pendulum vibrates most rapidly, 
when most influenced by gravity. So it has been found by experiments, 
that the force of electrical attraction and repulsion, varies as the square 
of the distance from the excited substance. The reciprocal action of mag- 
nets and the electrical fluids are, therefore, subject to the laws of mechanics. 

5th. Magnetism and electricity may both be communicated to other bodies 
by induction. But magnetism cannot, like electricity, be transferred from 
one body to another. By induction is meant, that magnets and excited elec- 
trics communicate their properties to other bodies in contact with them, by 
which process they are not, themselves, deprived of any portion of their mag- 
netism or electricity. By the transfer of electricity is meant, that an elec- 
trified body gives off its electricity to another body. The process of induc- 
tion is quiet ; while that of transference is accompanied by light and sound. 

6th. The phenomena of magnetism, like those of electricity, have been 
explained on the supposition of one fluid existing in the state of plus and 
minus, or positive and negative ; and the contrary hypothesis of two fluids. 
Those who advocate the hypothesis of one magnetic fluid, suppose that in 
the magnet, while there is a surplus at one end or pole, there is a deficiency 
at the other. The surplus or positive pole is said to be plus magnetic, and 
the deficient or negative pole to be minus magnetic. This is according to 
Franklin's theory of electricity. The theory of two magnetic fluids corres- 
ponding to the doctrine of the two species of electricity is now generally re- 
ceived. According to this, in the particles of iron, and in all bodies in which 
iron is found, are lodged two fluids or forces, the one predominating at one 
end, and the other at the opposite end ; each particle attracting those parti- 
cles in which the opposite fluid prevails, and repelling those in which a sim- 
ilar fluid resides ; and this attraction or repulsion is proportioned to the in- 
verse square of the mutual distances of the particles. 

Electro-Magnetism, 

676. Lightning and the Aurora Borealis, which are electrical 
phenomena, are observed to have great power in disturbing the po- 
larity of the compass ;* and it has recently been discovered by Pro- 

* At the time of the great Aurora Borealis of Jan. 25, 1837, the magnetic 
needle was observed to be remarkably distnrbed. 

676. Origin of the theory of electro-magnetism. Experiments made to 
prove the connection between electricity and magnetism. 



MARINEK S COMPASS. 271 

feasor CErsted of Copenhagen, that a current of galvanic electricity 
produces similar effects. This discovery has given rise to the the- 
ory of electro-magnetism. 

" The connection of electricity and magnetism," says Herschel, " had long 
been suspected, and innumerable fruitless trials had been made to determine 
the question. The phenomena of many crystallized minerals which become 
electric by heat, and devolop opposite electrical poles at their extremities, offer- 
ed an analogy to the polarity of the magnet, so striking, that it seemed hardly 
possible to doubt the connection of the two powers. The development of a simi- 
lar polarity in the voltaic pile, pointed strongly to the same conclusion. Of all 
the philosophers who had speculated on this subject, none had so pertinaciously 
adhered to the idea of a neeessary connection between the phenomena as CEr- 
sted. Baffled often, he returned to the attaek ; and his perseverance was at 
length rewarded by the complete disclosure of the wonderful phenomena of 
electro-magnetism. There is something in this which reminds us of the obsti- 
nate adherence of Columbus to his notion of the necessary existence of the new 
world ; and the whole history of this beautiful discovery may serve to teach us 
reliance on those general analogies and parallels between great branches of 
science, by which one strongly reminds us of another, though no direct connec- 
tion appears ; and that such analogies are indications not to be neglected, of a 
community of origin." 

677. Though the connection which exists between light and mag- 
netism is obscure, its existence is certain. It had been known, 
for many years that the violet ray of the solar spectrum has the 
power of rendering iron magnetic. In 1825, Mrs. Somerville, of 
England, made a series of experiments by which she proved that 
the indigo, blue, and green rays, as well as the violet ray, possess 
a magnetizing power.* 

Mariner's Compass. 

678. The most important application of magnetism is found in 
the mariner's compass. In order to trace the meridian line which 
may point out the north and south, recourse may be had to as- 
tronomical observations, as the motion of the sun and stars deter- 
mines that direction. But the heavenly bodies are sometimes ob- 
scured, and in darkness and storm, the mariner's compass is the 
only dependance of the seaman. Before its discovery long sea- 
voyages were not attempted ; for if the mariner lost sight of the 
shore, he might wander far from his native land, with no pathway 
upon the trackless ocean to direct his return, nor any index to 
point out the proper direction. Like a blind man attempting un- 
aided to grope his way to a distant city, he might be going in a 

* For a description of Morse's Electro-Magnetic Telegraph, see the Au- 
thor's stereotype edition of Familiar Lectures on Chemistry, page 68. For 
other late discoveries in this science, see the same work. 

677. Connection between light and magnetism. 

678. Utility of the mariner's compass. 



272 NATURAL PHILOSOPHY, 

direction opposite to the place of his destination. Without the 
aid of the compass, Columbus might vainly have reasoned upon 
the existence of another continent ; for, with all his boldness, he 
would never have dared to venture upon the untried ocean with no 
guide but the uncertain stars. 

679. The inventor of the mariner's compass is not known ; 
and it is even doubtful at what period, or by what nations, mag- 
netic polarity was used for determining the direction of places on 
the earth's surface. It is supposed that a rude form of the com- 
pass was invented by the Tartars, to guide them in their wander- 
ings over land ; and that they imparted a knowledge of the instru- 
ment to the Chinese. The Crusaders, on their return from the 
East, brought it into Europe, as they did many other valuable im- 
provements in the arts and sciences, gleaned among the remnants 
of once powerful and enlightened nations. 

680. The compass first used was a very imperfect instrument, consisting of 
pieces of the natural loadstone fixed on cork or light wood, so that it might float 
on the surface of the water in a dish, on which were marked the cardinal points 
of the compass. In the compass now used, the magnetic needle is placed 
within a small box of brass, covered with glass, and so fixed as to retain a hori- 
zontal position in all motions of 

Fiff. 272. ^ e S ^P* r ^^- e nee(He * s generally 

a thin, flat plate of steel, tapering 
towards each end, and, to prevent 
friction, turning on the point of an 
agate, one of the hardest of mine- 
rals, for a pivot. Beneath the nee- 
dle is a circular card, on which are 
described two circles, one divided 
into 360 degrees ; and the other into 
32 equal parts called points of the 
compass; of which the four, viz., 
north, south, east, and west, are 
called cardinal points, while inter- 
mediate between these are the points 
N E or north-east, S E or south- 
east, S W or south-west, N W or 
north-west ; N b E is north by east, 
N N E is north of north-east, N E b E is north-east by east, &c. 

681. The surveyor's compass, used in surveying land, and the 
pocket compass indispensable to the traveller in making his way 
through a pathless forest, are constructed upon the same princi- 
ples as the mariner's compass, modified so as to suit the uses for 
which they are intended. 

679. Inventor of the compass. 

680. First compass which was used. Compass now used. 

681. Surveyor's compass and pocket compass. 




PART VIII. 

CELESTIAL MECHANICS, OR ASTRONOMY. 



LECTURE XL. 

INTRODUCTORY REMARKS. ARMILLARY SPHERE. THE SOLAR 

SYSTEM. PLANETS. COMETS. APPLICATION OF ME- 
CHANICAL LAWS TO PLANETARY MOTION. 

682. Man is a being of so transient an existence, so limited in 
faculties, and so blind to the designs of the Almighty, that it seems, 
in no small degree, wonderful that he should presume to scan and 
measure the objects by which he is surrounded. The child, be- 
holding the canopy of heaven, feels a mysterious awe steal upon 
his spirit. He beholds that for which the surface of the earth 
around him has no parallel, and his feeble intellect becomes be- 
wildered in the contemplation of the celestial glories. There 
is connected with the study of the celestial bodies, a kind of re- 
verence, a feeling that we tread on consecrated ground. Were 
science for the first time about to scale the heavens, and attempt 
to measure the magnitudes, determine the motions, and compute 
the distances of its distant luminaries, how bold and hopeless would 
seem the enterprise ! Should we not exclaim, " It is enough for 
mortals to learn the nature of the terrestial objects around them, 
without presuming to understand the laws which govern the ce- 
lestial spheres." 

683. It is not left for the moderns to take the first steps in as- 
tronomy ; the ancients had much more correct notions of this sci- 



682. Reflections on commencing the study of celestial mechanics. 

683. Antiquity of astronomy. Impediment to its progress. 



274 NATURAL PHILOSOPHY. 

ence, than of the physical nature of the objects by which they were 
immediately surrounded. Man in the earliest ages was led to con- 
template the heavens ; — the shepherds of the east, in their night- 
watches on the plains of Babylon and Chaldea, made many im- 
portant observations on the motions of the celestial bodies. A new 
star, seen by the wise men of the east, was a token to them that 
the Messiah was born ; and following its guidance, they traveled 
westward, till the star stood over a little village of Judea called 
Bethlehem, " where the young child was." 

Astronomy was that branch of physical science which the 
ancients cultivated with most success. Notwithstanding their 
imperfect means of measuring time and space, they had learned 
the motions of the sun and moon so as to be able to predict eclipses 
with some degree of accuracy. The progress of astronomy was 
greatly impeded by the belief in the doctrines of Aristotle, which 
taught, that the celestial bodies, in their motions, were governed 
by laws peculiar to themselves, and bearing no analogy to those 
which regulate the motions of terrestial bodies. But there were 
those, who, from age to age, attempted to throw off the chains 
which bound the intellect of man ; and faint glimmerings of light 
occasionally broke forth, showing the true pathway of science. 

684. But it was not until the time of Newton, that the motions 
of the heavenly bodies were explained, by the simple law, " that 
every particle of matter attracts every other particle of matter in 
the universe, with a force proportionate to the product of their 
masses directly, and the square of their mutual distance inversely. 
This law once established, what before seemed regularity without 
a plan, appeared a beautiful and harmonious system. Philoso- 
phers were ready to ask, " is this all ?" and to wonder that they 
had not before discovered what was so simple. The true mecha- 
nism of the heavens was first taught, and proved by Newton. He 
not only established his theories by the most plain and conclu- 
sive arguments, but bringing mathematics to his aid, conclusive- 
ly demonstrated the truth of his propositions. 

The pupil must not expect in these familiar lectures, designed to give but the 
outlines of philosophy, an attempt to explain all the phenomena of the heavens, 
or to make him acquainted with but a small part of the brilliant discoveries 
which illuminate the Principia* of Newton, and the labors of his successors. 
Astronomy, though considered as a branch of Natural Philosophy, is of itself a 
vast and comprehensive science. Our object is to impart some knowledge of 
celestial mechanics, by which we mean those mechanical phenomena of the 
heavens, which may be explained by a reference to the laws of motion, attrac- 
tion, and gravitation. By these well established laws and principles, the revo- 

* Thi9 is the title of Newton's work on Natural Philosophy : to understand 
which has been called the test of a great mind. 

684. Newton's explanation of the laws of attraction. Newton's theories. 



CELESTIAL GLOBES. 275 

lutions of the planets and their satellites in their orbits, and their rotation on 
thoir axes, are all accounted for. 

6'85. Celestial mechanics may be defined, the science which 
teaches the magnitudes and distances of the heavenly bodies, their 
various /notions, and the laws by which they are governed. 

686. When we stand upon an open plain, and look around us, we perceive, on 
all sides, a circle where the earth and sky appear to meet. This circle is call- 
ed the horizon. On looking upwards, we see what appears a concave hemi- 
sphere. In the night it is spangled with brilliant gems, many of which seem 
less than tho diamond in a finger ring, while a body, which seems much larger 
than any of tho stars, illumines the earth with a mild but splendid light. In the 
day, all these lesser lights appear to have vanished, and one luminary with 
bright and piercing beams, alone is seen to move over tho blue concave vault. 

But all these appearances are, in a degree, illusory. What seems to be the 
blue sky, is, in reality, only the body of air around us which decomposes the 
rays of light from the sun, and, absorbing all the other rays, reflects only the 
blue. The tiny, twinkling star is, in reality, a sun, millions of times more vast 
in its dimensions than the world we live in. The moon, which looks larger than 
any star, is, in reality, the smallest of all the heavenly bodies which are seen 
by the naked eye. But the moon being much nearer to the earth, than any 
other celestial body, appears larger. Examine the moon through a powerful 
telescope, and you see, as if near us, a very large globe apparently suspended in 
air, and exhibiting on its surface the outlines of mountains, valleys, and even 
seas and volcanoes. In the day, there are stars in tho heavens above us the 
same as at night ; but the lesser lights of the heavens are not visible in the 
presence of the greater luminary 

Again, the celestial bodies appear to rise in the eastern horizon, mount up to 
the meridian, and then sink in the west; but it is, in reality, our own motion, 
and not theirs, which causes these phenomena. And the blue vault cf heaven is 
but an optical illusion. The stars, which seem set near each other in the etherial 
arch, are posted in various parts of infinite space, many millions of miles distant 
from us, and from each other, and are probably suns in the center of other sys- 
tems of worlds. The body of atmosphere which surrounds our globe, and through 
which rays of light from the celestial luminaries penetrate, extends but about 
forty-five miles in depth. Beyond this, we know not what may fill even the 
spaces between the globe of earth which we inhabit, and the neighboring planets 
in our own solar system. Some have imagined the existence of a subtle fluid, 
called ether, whose vibrations produce the impression of light. Others suppose 
a fluid which, moving in currents, impels the celestial bodies, and produces their 
various motions. But we can never demonstrate the truth of these hypotheses, 
at least, until some new discover)' shall give us powers which we do not now 



687. As the earth and its divisions are represented upon a 
sphere called the terrestrial, globe, so the heavens are delineated 
upon a celestial globe exhibiting the situation of the various clus- 
ters of stars which appear there. 

685. What is the science of celestial mechanics ? 

686. Appearance of the heavens. Difference between appearance and re- 
ality in respect to the heavens. Why the stars are not visible in the day. 
Apparent motion of the celestial bodies. Cause of the apparent moiion. 
Distance of the celestial bodies. Hypothesis of fluids beyond our atmo- 
sphere. 

687. Celestial globe. 



276 



NATUKAL PHILOSOPHY. 



Fig. 273. 



7,cnrtTt 



But the convex surface of a celestial globe represents the apparent concave 
of the heavens, and therefore must fail to give us -correct notions of actual ap- 
pearances. Some of the universities of Europe are furnished with celestial 
globes sufficiently largo to admit several persons within. On the inner surface 
are painted the celestial bodies, and the various circles which astronomers ima- 
gine in the heavens. By the revolution of this artificial sphere, the spectators 
within, see stars rise, ascend, and set, as they appear to do in the real hemi- 
sphere. 

688. That point of the heavens over head is called the zenith ; 
the point directly opposite, or under foot, is called the nadir. 

The fixed points round which the sphere of the heavens is sup- 
posed to turn, are the poles of the celestial sphere, or of the hea- 
vens, and a line drawn from one pole to the other, is called the 
axis of the heavens; around this line the celestial bodies seem 
to revolve every day. 

689. The Armillary 
Sphere* This is a re- 
presentation of the earth 
as situated within a revolv- 
ing sphere, (Fig. 273,) 
where various lines and 
circles are delineated. 

1st. The axis of the earth. 
This is an imaginary line 
passing through the earth's 
center, and extending on 
each side, to the poles of 
the celestial sphere. 

2d. The meridian. If 
you point directly over 
head and move your finger 
towards the south pole, 
you will describe a line 
which the sun crosses just 
at noon. This line is call- 
ed a meridian. Suppose 
this line extended so as to 
form a complete circle a- 
round the heavens ; it is evident that all the celestial bodies must 
"ross this meridian twice in 24 hours. The sun crosses it at mid- 




From the Latin armilla, a bracelet, ring or circle. 



688. Zenith and nadir. Poles of the celestial sphere. Axis of the 
heavens. 

689. Armillary sphere. Axis of the earth. Meridian. Equator. Zodiac. 
Horizon. Colures. Polar circles. Tropics. 



CELESTIAL GLOBES. 



277 



night as well as at noon ; and the star which we may see cross- 
ing our meridian at midnight, will, at noon, cross the meridian on 
the opposite side of the globe. The figures on the meridian re- 
present degrees. From the equator to each pole, is one quarter 
of the celestial sphere, or 90° ; and no star can be more than 
ninety degrees distant from the horizon. 

3d. The Equator or equinoctial line, is a broad belt encircling 
the middle of the earth from east to west. 

4th. The Zodiac or ecliptic, represents the sun's apparent path 
in the heavens ; this is the earth's real path or orbit. 

5th. Horizon ; this astronomical circle is called the rational or 
true horizon, and represented as encompassing the globe in the 
middle, or as 90° distant from the zenith and the nadir. It is re- 
presented on the artificial globe by a broad plane of wood. This 
horizon is distinguished from the circle where the sky appears to 
touch the earth and sea, called the sensible horizon. 

6th. The two Colures, are two meridians which pass through 
the poles of the sphere ; they are called the equinoctial* and solsti- 
tial\ colures. The equinoctial colure passes through two points 
in the heavens, called the vernal and the autumnal equinoxes. 
When the sun arrives at either of these points, the nights are of 
the same length as the days. The solstitial colure passes through 
two points called solstitial points ; because when arriving at either 
of those points, the sun seems to remain stationary for several days. 

7th. Arctic and antarctic circles, are northern and southern polar 
circles at the distance of 23£ degrees from the poles. 

8th. Tropic of cancer and tropic of Capricorn, are circles par- 
allel to the equator at the distance of 23^ degrees from it. 

690. The earth appears in the center of the celestial sphere. In terrestrial 
globes, the various circles delineated in Fig. 273, are usually marked on the 
surface, except the meridian, which is a brazen circle surrounding the globe, 
and dividing it into eastern and western hemispheres, and the horizon, which 
is a circular plane of wood dividing the globe into upper and lower hemispheres. 
By observing the ecliptic and other circles drawn on the surface of the terres- 
trial globe, or a map of the earth, the pupil often acquires erroneous ideas. 
The figure in which wo have represented the astronomical circles may rectify 
these notions. There is no real axis passing through the earth or the celestial 
sphere. The ecliptic or path of the earth around the sun is assumed for astro- 
nomical purposes. The earth in its rapid motion around the sun, in reality no 
more leaves a track to mark its pathway, than the ship leaves its traces upon 
the pathless ocean. But yet for nearly 6000 years has the earth pursued one 
undeviating course, completing with perfect regularity its annual revolution. 
The cause of the planetary motions we shall consider after having made 

* Equinoctial, literally signifies equal nights. 

t Solstitial, literally signifies, the sun standing still. 

690. Manner in which the circles described are usually represented on the 
artificial terrestrial globe. How may erroneous ideas be acquired? 

24 



278 NATURAL PHILOSOPHY. 

some observations on the celestial bodies which, in their united effects upon each 
other, produce these motions. 

THE SOLAR SYSTEM. 

B91. Astronomers suppose that the universe is composed of an 
infinite number of systems, or families of worlds, each sun being 
connected with every other planet in its system or family, by ties 
that cannot be broken without throwing the whole into confusion. 

Of other systems than our own, little is yet discovered. It is 
supposed that each fixed star is a sun, and the center of its own 
system of worlds. 

Our system is called the solar system, and consists of the sun 
with its planets,* and their attendants, called satellites or rnoons. 

The Sun. 

692. The sun is the center of the solar system, and the source 
of light and heat. It is the center of attraction which connects 
and binds together the whole solar system. Its magnitude is 
more than a million of times greater than that of the earth ; and 
it is ninety-five millions of miles distant from it. The sun was 
long supposed to be an immense globe of fire. Some eminent 
astronomers of the present day believe it to be an opaque body 
surrounded by a highly luminous atmosphere. What it is, we 
know not. As its great Creator pervades every place throughout 
the universe, and yet has his seat in the heavens, so the sun, by 
his rays, is in all places throughout the solar system, while he is 
fixed in the center of that system. The sun, like the earth, re- 
volves on its axis, and completes one revolution in 25 days. This 
is proved by observing certain remarkable spots on the sun's disc. 
These spots are seen to appear and disappear at regular intervals, 
which can only be accounted for by supposing a rotation on its axis. 

The sun, if viewed from any other system in the universe, would 
appear, to beings with the same optical powers as we possess, as 
a fixed star does to us. 

The Planets. 

693. Between the earth and the sun are two planets, Mercury 
and Venus. These are called inferior planets, because their or- 

* From the Greek planetes, wandering or moving. 

691. Opinions of astronomers with regard to the universe. Solar system. 

692. The sun. Magnitude of the sun. Revolution of the sun. Probable 
appearance of the sun at other systems. 

693. Inferior planets. Mercury. Venus. Transit of Venus. 



SOLAR SYSTEM. 279 

bits are nearer the sun than is the orbit of the earth, or, in other 
words, they are within the earth's orbit. 

Mercury is the most rapid in its motion of all the planets, and, 
for this reason, was named by the ancient heathen after the swift 
messenger of the gods. 

Venus, during one part of the year, is Lucifer, or the morning 
star, and at another portion of the year, Hesperus, or the evening 
star. She is the morning star when seen westward of the sun, 
for she then rises before that luminary. She is the evening star 
when seen eastward of the sun, for she then sets after him. As 
the orbit of Venus lies between the earth and the sun, it follows 
that when she passes across the sun's disc, a dark round spot ap- 
pears to as on that luminary. This is called the transit* of Venus, 
and has occurred only twice in about 120 years ; the last time 
was the 3d of June, 1769. In the present century there will be 
two transits of Venus ; one in the year 1874, and the other in 
1882. By the observation of this phenomenon many important 
astronomical calculations have been made. 

694. The Earth is the third planet in the solar system. To an in- 
habitant of Venus our planet would appear much as Venus does to us. 

Looking on onr earth as a star in the solar system, we are at once undeceiv- 
ed as to the apparent motions of the heavenly hodies around it. Can we sup- 
pose that the vast orb of the sun, with the planets in its system, some of which 
are much larger than the earth, are all satellites to our little world? Reason 
smiles at the supposition, and philosophy pronounces it impossible. The smalier 
body, according to the principle of gravitation and the laws of motion, must re- 
volve around the larger. 

The moon is a satellite of the earth. Like the other heavenly 
bodies it daily alters its apparent position, and, in the course of a 
month, appears to make a complete revolution round the heavens 
from west to east, while, at the same time, it has, like the iixed 
stars, an apparent, daily motion from east to west. Of all the ce- 
lestial luminaries, this is the nearest to us, its mean distance being 
about 237,000 miles. When the moon, in her revolution in her 
orbit, passes between the sun and the earth, the sun's light is par- 
tially or totally hidden from the earth, and this is called an eclipse 
of the sun ; — when the moon falls into the earth's shadow, so that 
she is not enlightened by the sun, an eclipse of the moon is caused. 

695. The planets in the solar system whose orbits are beyond 
that of the earth, are called superior planets ; these are Mars, Ju- 
piter, Saturn and Herschel, with four smaller, and lately discov- 
ered planets, called asteroids. 

* From trans, passing over. 

694. The earth considered as a star in the solar system. The moon and 
her revolutions. Cause of an eclipse of the sun. Of the moon. 

695. Superior planets. Mars. Jupiter. Eclipses of his satellites. 



280 NATURAL PHILOSOPHY. 

Mars has no satellite, and is known by his deep red color. 

Jupiter is the largest of all the planets, and is attended by four 
moons or satellites. He is distinguished in the heavens for his 
magnitude and brightness, being scarcely less bright than Venus. 
When examined through a telescope his surface seems shaded by 
stripes. Some astronomers suppose these to be the effect of 
changes in the atmosphere of the planet ; others that they indi- 
cate some great physical changes which are taking place on its 
surface. By the eclipses of Jupiter's satellites, light, which was 
formerly supposed to move instantaneously, is found to have a pro- 
gressive motion. By observations upon these eclipses, with the 
help of optical instruments, the mariner, when other means fail, 
may determine the degree of longitude. 

696. Saturn shines with a pale light ; he is attended by seven 
moons, and is remarkable for being surrounded with a double ring, 
more luminous than the planet itself. This ring revolves around 
the planet, it is more than 33,000 miles broad, and not quite 300 
miles in thickness, so that it resembles a broad plane. No part of 
its surface is nearer than about 2300 miles to the surface of the 
planet. From its great extent, we may reasonably believe it to be 
a world of itself, and peopled with intelligent beings. 

697. Herschel, sometimes called Uranus,* and Georgium Si- 
dus,* was discovered as late as 1781, by the celebrated astrono- 
mer, Dr. William Herschel, who with his sister, Miss Caroline 
Herschel, and his son, Sir John Herschel, form a constellation of 
talent in the department of astronomy. The planet Herschel is 
so immensely distant from this earth as to be scarcely visible with- 
out a telescope. It has six moons or satellites. Beyond the orbit 
of Herschel no planets have yet been discovered in the solar 
system. 

698. The asteroids revolve around the sun in orbits which are 
between the orbits of Mars and Jupiter. They are called Vesta, 
Ceres, Pallas and Juno. 

Comets. 

699. Comets are bodies which move around the sun in very 
long elliptic curves, sometimes approaching near the sun, and then 

* Uranus, in mythology, is the father of Saturn. Georgium Sidus, literally 
the Georgian star, was a name given by Dr. Herschel, in compliment to his 
sovereign, George III, King of Great Britain. 

696. Saturn. His ring. 

697. Herschel. When discovered. 

698. Asteroids. 

699. Comets. Enke's comet. Comet of six year's period. Halley's 
comet. 



MAGNITUDE OF THE PLANETS. 281 

travelling far beyond the orbit of the most distant planet. Among 
hundreds of comets which have at different times been visible, the 
revolutions of three only, have been determined with any degree 
of accuracy. One of these called Enke's comet, has a period of 
three years and 112 days ; it is very small, and seldom visible to 
the naked eye. Another comet, which has a period of six years 
and three-fourths, appeared in 1822. Halley's comet appeared in 
1835. The great astronomer whose name it bears, ascertained 
the period of its revolution to be about 75 years, sometimes a frac- 
tion of a year more, and sometimes less. For the astronomer in 
computing the motions of comets must take into the account, be- 
sides the usual rate of motion in different parts of their orbits, the 
delays which they may receive from the attractive forces of the 
various celestial bodies, within whose spheres of influence they 
may happen to fall. Thus Halley's comet, in one of its revolu- 
tions round the sun, was delayed or retarded one hundred days 
while within the sphere of attraction of the planet Saturn, and five 
hundred and eighteen days while within that of Jupiter. 

700. Comets are accompanied by a train of light resembling il- 
luminated hair,* called the tail of the comet. By some, the comet 
itself is supposed to be a nucleus of vapors, and the train or tail, 
which appears somewhat like the aurora borealis, to have its ori- 
gin, as that meteor is supposed to have, in disturbed electricities. 
But nothing certain is known as to the physical constitution of 
these bodies. If comets are peopled, the beings who inhabit 
them must be fitted to endure the greatest diversity of climate ; 
from the burning heat of the sun when nearest to that luminary, 
to the total absence of heat, when traversing the distant and ut- 
most boundaries of the solar system. They must endure also, the 
change of being sometimes carried onward with a velocity almost 
equal to that of a ray of light, and then ith the slow pace with 
which the comet moves in the utmost point of its orbit. 

Proportional Magnitude of the Planets, 

701. The Earth is fourteen times as large as Mercury, very 
little larger than Venus, and three times as large as Mars. The 
diameter of Jupiter is 1 1-|- times greater than the diameter of the 
earth; its surface is 118 times, and its bulk 1281 times greater 

* Whence the name, from the Latin coma, a hair. 

700. Comet's train. Physical constitution of comets. 

701. Slate the comparative magnitudes of the planets. State the distan- 
ces of the planets from the sun. In how long a time would a cannon ball 
moving at the rate of eight miles a minute go from the sun to Mercu- 
ry, &c. 

24* 



282 



NATURAL PHILOSOPHY, 



than that of the earth. The bulk of Saturn and his ring united is 
more than 1000 times greater than the earth. The surface of 
Herschel is 19 times larger than the earth, but this planet is much 
less solid, so that its quantity of matter is only about seventy-eight 
times greater than that of the earth. 

Distances of the Planets from the Sun, in miles. 



Mercury, 
Venus, . 
Earth, . 

Mars, . . 
Vesta, . . 



. 37,000,000 
, 68,000,000 
, 95,000,000 
143,000,000 
225,000,000 



Juno, Ceres, 
Pallas, 
Jupiter, . . 
Saturn, . . 
Herschel, . 



I 261,000,000 

. . 490,000,000 

. . 900,000,000 

. 1,800,000,000 



Fig. 274. 




That we may more 
easily comprehend the 
vast distances of the 
planets from the sun, 
some rule or measure, 
adapted to the capa- 
city of our senses, must 
be resorted to. Thus, 
reckoning the velo- 
city of the cannon ball, 
at 8 miles a minute, 
it would go from the 
sun to Mercury in 9£ 
years ; from the sun 
to Venus in 18 years ; 
to the Earth in 25 
to Mars in 38 
to Vesta in 60 
to Juno in 66 
to Ceres and 
Pallas in 69 years ; to 
Jupiter in 130 years ; 
to Saturn in 238 
years, and to Herschel 
in 479 years. A can- 
non ball with the stat- 
ed velocity, would go 
from the earth to the 
moon in 23 days. 

702. By means of an 
orrery is represented the 
motion of the planets a- 



years ; 
years ; 
years ; 
years ; 



702. Explain the orrery. 



DECREASE OF ATTRACTION. 283 

round the sun, and that of the satellites around the primary planets, with 
their comparative magnitudes and distances. 

On the upper plate, which answers to the ecliptic, are placed, in two oppo- 
site but corresponding circles, the days of the month, and the signs of the zo- 
diac with thoir respective characters. By this plate, the planetary balls may 
be so set as to be in their proper places on the ecliptic for any day in the year. 
A brass ball in the center represents the sun, this is supported by a brass rod 
which passes through the center of the plate, and has sockets for supporting the 
arms by which the several planets, with their satellites are supported. The 
planets are represented by ivory balls, having the hemisphere which is towards 
the sun white and the other black, to represent their different phases. The 
moons or secondary planets are arranged in the proper order around the pri- 
mary planets. 

By turning the handle of the orrery, a train of wheel-work, which is con- 
cealed in the circular brass box under the upper plate, is set in motion. The 
planets revolve around the sun in the center, and the moons revolve around 
the planets. To give a more perfect representation of the solar system, the 
planets with their respective moons, should have a rotary motion on their axes. 

703. Instead of a motion from east to west, which the celestial 
bodies appear to have, they actually revolve around the sun, and 
upon their own axes, from west to east. The. earth also revolves 
in the same manner. This motion of the earth from west to east, 
makes the sun appear to us to move around us in a contrary di- 
rection ; as when we start in a steamboat from New York to go 
up the Hudson, the city itself appears to be moving southwardly, 
when, in reality, it is our own motion towards the north which 
causes this appearance. 

Application of Mechanical Laws to Planetary Motion. 

704. The attraction of gravitation is in proportion to the quan- 
tity of matter. The sun being the largest body in the solar sys- 
tem, attracts the planets, and they, in turn, gravitate or tend to- 
wards the sun. 

705. Attraction decreases, as the squares of the distance in- 
crease. Suppose a planet at B, to be twice as far from the sun as 

Fig. 275. 

cr k^— 

at A ; then, as the square of the distance 2x2 is 4, the attraction 
at B will be four times less than at A, or which is the same thing, 
the planet at A will be attracted with four times the force it would 
be at B. But if the distance of A from the sun were four times 
less than that of B, then as the square of 4x4 is 16, the attrac- 
tion at A would be sixteen times greater than at B. 

703. Real motion of the celestial bodies. Motion of the earth. 

704. Law of gravitation. The sun and planets mutually attracted. 

705. Decrease of attraction. 



284 NATURAL PHILOSOPHY. 

706. Since the planets are attracted towards the sun with a 
force proportioned to his quantity of matter, and their respective 
distances, why, it may be asked, do they not fall upon the sun, as 
bodies attracted by the earth, fall upon its surface ? To solve this 
question, you will have occasion to recall what has been said of 
the effect of motion produced by two forces. Motion produced by 
one force, you have learned, is in a straight line ; but the planet- 
ary motions, in their orbits, are circular. The planets do not fall 
upon the sun, because there is, in operation, another force besides 
that of gravitation which affects their motion. This is the pro- 
jectile or centrifugal force, while the sun's attraction is the centri- 
petal force; the joint action of these forces, produces the circular 
motion of the planets, and keeps them in their orbits. Thus, sup- 
pose a stone whirled around in a sling ; we 

Fig. 276. have a circular motion resulting from two 

forces ; 1st. the projectile force which was 
first given it by the arm, and 2d. the central 
force, or that with which it is held by the 
string. If the stone flies out of the sling, the 
projectile force alone would then act, and the 
stone would move from A to a, or in a tan- 
gent to the circle ; if let go at B, the stone 
would move in the tangent B b, or at C, in 
the tangent C c. 

By this law, the moon moves round the 
earth, and the earth and other planets move round the sun ; the 
projectile force and the force of gravitation being so nicely bal- 
anced, as to retain them in their orbits. Should one of these 
forces cease, the other would then act alone, the projectile force 
unbalanced, would carry the earth, in a straight line, off into in- 
finite space ; while the force of gravity alone would cause it to 
fall upon the sun. 

707. The orbits of the planets are not perfect circles, but ellipses 
or ovals, that is, having greater length than breadth, and with two 
central points, called foci. Suppose a planet, A, (Fig. 276,) moving 
by its projectile force towards B, if it met with no resistance, it would 
forever move on in a straight line, and would pass in equal times 
over equal spaces, that is, from B to C in the same time as from 
A to B, and so on. But at B, it is acted on by a new force, viz., 
the sun's attraction in the line S B. The two forces acting at the 
right angle A B S would, if equal, cause the planet to revolve in 

706. Circular motion of the planets, bow produced. Effect of disturbing 
either of the two forces which keep the planets in their orbits. 

707. Elliptical orbits of the planets. Explain the motion of a planet in 
its orbit. 




285 



Fig. 277. 




the circle BEF; but the sun's attraction being more powerful 
than the projectile force, the planet is brought nearer the greater 
force, and describes the curve B G. Now at G the angle O made 
by the two forces is less than the right angle, in conseqence of the 

forces acting more in concert, the 
motion in this part of the planet's 
orbit is acellerated ; and further, as 
the distance of the planet from the 
sun decreases, attraction increas- 
es. At the point M, the increased 
velocity has increased the centrifu- 
gal force so much, that the planet, 
would be impelled in a tangent to- 
wards D, were it not that the force 
of attraction is constantly becom- 
ing greater. Thus the motion of 
the planet is uniformly accelerat- 
ed from B to H. At H the pro- 
jectile force is so great that it 
would impel the planet to I, while 
the attractive force would draw it towards S, but the joint action of 
the two forces carries it to L. In passing from H to B, or in going 
from the sun, its motion is retarded in the same degree that it was 
accelerated from B to H, so that at H or nearest the sun, the ve- 
locity is greatest, while at B it is least. 

708. Thus the elliptical orbits of the planets are caused by a 
projectile force, and the repeated action of gravitation which draws 
the body from a true circle. A circle has within it one central 
point, which is equally distant from every part of its circumference ; 
but an ellipsis has two central points called foci.* 

The sun (Fig. 277) is in the lower focus of the ellipsis 
BGH. When the planet is nearest the sun, as at H, it is said 
to be in its perihelion ; when most distant, as at B, in its aphelion. 

709. If the attractive powers of the sun were uniformly the 
same in every part of the orbits of the planets, they would pass 
over equal spaces in equal times. But on account of being more 
attracted in some parts of their orbits than in others, the planets 
pass over unequal portions of their orbits in equal times. But the 
areas which are included in those spaces are equal, that is, the 
area of the triangle B S W, is equal to the area of the triangle 

* Plural of focus. 

708. Cause of the elliptical orbit of the planets. Foci of an eclipse. Peri- 
helion. Aphelion. 

709. Explain what is meant by the planets passing over equal spaces in 
unequal times. 



286 NATURAL PHILOSOPHY. 

LSH, although the arcs which subtend these triangles are un- 
equal. If the twelve triangles made by the lines proceed- 
ing from the circumference B M H to S be considered as re- 
presenting the twelve months in the year, we perceive that the 
spaces through which the sun passes will be increased each 
month for one half of the year, and proportionally diminished the 
other half, though the areas passed over in each month are equal. 
It is one of the great laws of planetary motion, that the planets, in 
their revolutions, describe equal areas in equal times, 

710. The secondary planets in their revolutions round their 
primaries, are governed by the same laws as those which cause the 
revolutions of the primaries around the sun. Thus the moon, be- 
ing within the sphere of the earth's attraction, and acted upon also 
by a projectile force, is retained in her orbit, and continues to re- 
volve around the earth. The secondary planets move with their 
primaries around the sun. 

711. It is conjectured that the sun himself, with his retinue of 
eleven primary planets, and eighteen satellites, sweeps around 
some grand center towards which solar systems gravitate, as 
planets gravitate towards their center ! But in pursuing such 
suggestions, 

" Imagination's utmost stretch, 
In wonder dies away." 



LECTURE XLI. 

FIXED STARS. CONSTELLATIONS. GALAXY. NEBULA. 

CONCLUDING REMARKS. 

712. We have briefly noticed the bodies which compose the 
solar system, or that family of worlds with which our own is 
connected. But these worlds are few in number, compared with 
the whole glorious company of celestial bodies, which we behold 
with the unassisted eye, when looking at the heavens in a clear 
night. The planets shine with a steady light, while the fixed stars 
are distinguished by their twinkling. The light of the moon is 
more steady and mild than that of the sun; the cause perhaps is 

710. Revolutions of the secondary planets. 

711. Probable revolution of the whole solar system. 

712. Bodies in the solar system few in comparison with the whole num- 
ber of stars seen by the naked eye. Light of the fixed stars and planets. 



■ FIXED STABS. 287 

that the moon shines by reflected light, and the sun by its own 
powerful rays. The planets arc all moons to us in respect to the 
reflection of light. The iixed stars are supposed to be all suns, 
shining with their own beams. The twinkling of the fixed stars 
is by some ascribed to the refractions and reflections produced by 
a variety of atmospheres. The planets seem as large, or larger 
than the fixed stars, because they are comparatively very near us. 

713. All the celestial bodies beyond our system are called fixed 
sta?s, because they do not appear to change their places in the 
heavens as the other planets do. This fixed appearance is probably 
owing to their immense distance from the earth. The orbit of the 
earth is twice ninety-five millions of miles across, and we are 
therefore one hundred and ninety millions of miles nearer to some 
stars at one time than at another, yet they always appear to be in 
the same places ; that is, the star which we see in the north, is 
always seen in the same latitude in the heavens ; that which we see 
at one time near the equator of the heavens, is always seen so, and 
that which we see in the south never appears in the north. 

If the circle A B represents the earth's 

Fig. 278. orbit, the earth at A will be one hundred 

and ninety millions of miles nearer to the 

^-^fcC*^. fixed star C, than it will be at B, and yet 

//** ~^^x tne ma g mtu d e °f tne star does not seem 

a. n. diminished by this distance, nor should we 

/^®"X A perceive any change in its position, if in 

I f g% \ 1 reality it were to move from C to D, be- 

, I IfliF J j cause this change would be nothing in 

^ ^b-^ j comparison to the distance of the star from 

VJ the earth. Two stars which seem to be 
>(/ very near each other, may be millions of 

~~~ lf ~~' miles distant, or one may be far beyond 

the other in the depths of space. The apparent motion of the 
stars from east to west, is caused by the earth's motion on its axis 
from west to east. 

714. The fixed stars, are supposed to be, like the sun of our 
system, centers of attraction around which revolve worlds with 
their attendant moons, and eccentric comets. These systems 
may be revolving in the immensity of spac°, but if so, our own is 
also pursuing the same round, and thus the relative positions of each 
are maintained. 

715. The stars have been arranged by astronomers according 

713. Fixed stars appear stationary. The cause of this appearance illus- 
trated. 

714. Fixed stars supposed to be suns. 

715. Classes of stars according to magnitude. Sirius. 



288 



NATURAL PHILOSOPHY. 



to their magnitudes and apparent brightness, into six classes. 
Thus Sirius, or the dog star, is said to be a star of the first mag- 
nitude. It is estimated, by some very nice calculations of Dr. 
Wollaston, that if this star were placed where the sun is, he 
would appear to us three times as large as that luminary, and give 
more than thirteen times more light. It is supposed that many of 
the fixed stars must be millions of times larger than Sirius. 
These are calculations indeed which almost overwhelm the reason 
of man ! They should humble that arrogance which seeks to find 
out " the hidings of Almighty power," and refuses to believe what 
human reason cannot comprehend. 

716. Stars of the sixth magnitude are the smallest which can 
be seen without a telescope. They may, in reality, be much larger 
than those that appear to us of the first magnitude ; their dimin- 
ished size being the effect of their immeasurably greater distance. 
By the naked eye, only about two thousand stars are visible, though 

when we look at the heavens 



Fig. 279. 




in a clear star-light night, 
their number seems beyond 
the power of computation. 
But this is an optical illusion, 
arising from the countless re- 
flections and refractions to 
which light from the stars is 
subject before it reaches us. 
On looking at a star of the 
first magnitude through a 
long narrow tube, the star 
will appear scarcely visible ; 
this shows that very few di- 
rect rays of the stars reach 
us, but that the brilliancy of 
the heavens is greatly owing 
to the reflection and refrac- 
tion of light. 

717. The astronomical tel- 
escope has revealed the heav- 
ens under a new aspect. Our 
solar system has been en- 
riched with new planets, the 
satellites and Saturn's rings 



716. Stars of the sixth magnitude. Number of stars visible to the naked 
eye. Cause of their appearing more numerous than they really are. 

717. Discoveries by means of the telescope. Parts of the astronomical 
telescope. Why objects seen through the telescope appear magnified. The 
moon seen under an angle of fifty degrees. 



THE CONSTELLATIONS. 289 

have been discovered, and the moon's surface is found to be di- 
versified by mountains and plains. 

Pig. ii7t3 represents a refracting telescope fitted up for astronomical observa- 
tions, in the manner practised by astronomers. Suppose A A to be a large 
tube, into which is inserted the small brass tube D, containing the eye-glasses. 
The object-glass is fitted to the upper end of the large tube ; h k are two han- 
dles for adjusting the instrument, and i I are for the purpose of keeping it steady. 
In considering the subject of optics, we noticed the construction and operation 
of telescopes. The glasses, or lenses, are so formed, that objects seen through 
them appear at a greater angle than when viewed with the naked eye ; this 
causes them to appear larger and nearer. Tho moon when viewed by the 
naked eye, appears under an angle of about half a degree ; therefore a telescope 
which represents it under an angle of fifty degrees, magnifies one hundred times. 

718. "The first result of the invention of the telescope, and its 
application to astronomical purposes by Galileo," says Sir John 
Ilerschel, "was the discovery of Jupiter's disc and satellites, — of 
a system offering a beautiful miniature of that greater one of which 
it forms a portion, and presenting to the eye of sense, at a single 
glance, that disposition of parts which in the planetary system 
itself, is discerned only by the eye of reason and judgment. We 
have here in miniature, and see at one view, a system similar to 
that of the planets about the sun." 

The Constellations. 

719. There has ever been in the mind of man a tendency to 
generalize and classify. Minerals, plants, and animals are group- 
ed together according to certain principles of resemblance. A 
collection of families is called a town, and many towns form a state. 
Even savages group themselves together in tribes. Following 
this bent of the human mind to generalize and classify, the priests 
and learned men of ancient Egypt, under their serene and cloud- 
less sky, and the ancient herdsmen and shepherds while tending 
their flocks and herds by night upon the plains of Chaldea and 
Babylon, observing the stars clustered together in groups, began to 
parcel out the heavens into various divisions, which they called 
constellations, and which they named according to their own pe- 
culiar fancies. 

720. In the book of Job, (which is considered one of the most 
ancient of the Holy Scriptures,) the constellation Orion, and the 
Pleiades, are named, with " Arcturus and his sons." Orion is 
perhaps of all the constellations visible in a winter's night, in our 

718. First application of the telescope to astronomy. 

719. Tendency of mankind to form classes. Origin of the arrangement 
of stars in constellations. 

720. First mention of constellations. Orion. How represented on tho 
celestial globe. Appearance of Orion in the heavens. Principal stars in 
Orion. Bands of Orion. Triangle in the head of Orion, &c. Discoveries 
made by the telescope in the constellation Orion. The Pleiades. The 
Hyades. 

25 



290 



NATURAL PHILOSOPHY. 



hemisphere, the most brilliant and the most generally known. 
Not perhaps so well known by its scientific name, as by that of 
the "yard and ell" and sometimes the "three stars." Many a 
thoughtful youth pauses in his winter sports upon the ice, to con- 
template this grand constellation, as it spreads itself across the 
eastern sky. In spite of the mirth of his noisy companions, his 
with inquiries as to the nature of those bright 
part they are fulfilling in the economy of the uni- 



soul is filled 
orbs, and the 
verse ! 



Fio-. 230. 



Orion is represented (see Fig. 280,) 
by the figure of a warrior, with a sword 
in his belt, a club in his right hand, 




and the head and skin of a lion in his 
left, for a shield. He seems to defend 
himself from the bull, the figure of 
which is represented in the constella- 
tion Taurus. Orion begins to appear 
in the eastern horizon, before nine 
o'clock in the evening, in the early part 
of winter. Every evening he is seen 
higher and higher in the heavens, until, 
on the 24th of January his most north- 
ern star appears on the meridian ; the 
center of the constellation is directly 
over the equator of the earth, and half 
way between the poles of the heavens. 
Four bright stars in the form of a paral- 
lelogram form the outlines of the constel- 
lation. The two upper stars are con- 
sidered as epaulets upon the shoulders of Orion, the western of the two lower 
stars is upon his left foot, the other upon his right knee. But this constellation 
is remarkably distinguished by the three bright stars in a row. which form the 
belt of Orion. They are in the middle of the parallelogram ; and they are 
beautifully described in the book of Job, as the bands of Orion. "Canst thou 
loose the bands of Orion ?" inquired the Almighty, of his presumptuous servant! 
The three stars in the belt measure just three degrees in the heavens, and ex- 
tend from north-west to south-east. 

In the head of Orion, is a triangle of three small stars, which form a large 
triangle with the two in his shoulders. The two upper stars in the parallelogram 
are about 15 degrees north of the lower ones. The name of the star in the left 
foot on the west is Rigel ; it is a star of the first magnitude, as is also the star on 
the east shoulder. The stars on the belt are of the second magnitude, those in 
the sword of the fourth and fifth magnitude. 

All that we have described of Orion, is plainly to be seen with the unassisted 
eye. But the telescope has revealed more than two thousand stars in this one 
constellation. One single star in the sword has been multiplied to twelve ; and 
in the belt no less than eighty stars have been discovered. Imperfect as the 
best instruments ave, and almost infinitely distant as is this constellation from us, 
how absolutely unlimited seems the number of stars which are clustered toge- 
ther in this jieighhorhood .' A neighborhood of stars of which the nearest art) 
millions of miles distant ! 

The Pleiades, or seven siars^ are a cluster which lie in the 
shoulder of Taurus, (the Bull,) to the north-west of Orion ; they 



CONSTELLATIONS IN THE ZODIAC. 291 

appear on the meridian a few minutes before 9 o'clock, on the first 
of January. The sun enters this cluster of stars in the spring, or 
season of blossoms, hence the inquiry of Job, " Canst thou bind 
the sweet influences of the Pleiades?" In this cluster of seven 
stars, as seen by the naked eye, more than two hundred stars have 
been discovered by the aid of the telescope. 

The Hyades are in the head of the Bull, eleven degrees south- 
east of the Pleiades. The cluster is composed of five stars, so sit- 
uated as to form the letter V. In this cluster is the red star Alde- 
Imran, a star of the first magnitude. The constellation Taurus, 
or the Bull, is represented as only exhibiting the head and shoul- 
ders of the animal. 

721. The heavens are divided by astronomers into three re- 
gions. The northern and southern portions, and the Zodiac* 
The Zodiac is a zone or girdle in the middle of the heavens, six. 
teen degrees broad, or eight degrees on each side of the ecliptic. 
The orbits of all the planets are within this zone. The ecliptic is 
the earth's orbit, or line described by the earth's annual revolution 
round the sun. In ancient times, long before men had any .true 
notions of astronomy, they supposed the sun moved around the 
earth, as indeed on account of the earth's motion it appears to do ; 
and observing that at different seasons, it appeared in different 
clusters of stars, they called these the signs of the Zodiac. 

Constellations in the Zodiac. 

722. The first astronomers seeing the sun in March always 
rise with a particular cluster of stars, called this cluster the con- 
stellation Aries, (the ram ;) thus they said the sun is in Aries in 
March. In April the sun rose in another constellation, which 
they called Taurus, (the bull;) and in May it rose in the constel- 
lation called Gemini (the twins.) These were the spring months ; 
and the names given to the constellations, were perhaps on ac- 
count of some fancied resemblance of their outline, to the objects 
after which they were called ; or from some relations of analogy 
connected with their agricultural or other pursuits, at the times 
when the sun successively rose with the twelve signs of the Zodi- 
ac. Thus the first signs, Aries and Taurus, are named after the 
animals which the shepherds and herdsmen, who were probably 
the first observers of the stars in reference to their influence upon 

* From the Greek Zodiakos, signifying an animal, The 12 signs of the 
Zodiac being represented by 12 animals. 

721. The heavens divided into different regions. 

722. Signs of the Zodiac. Signs which distinguish the spring months, 
Why were these signs thus called ] 



292 NATURAL PHILOSOPHY. 

the seasons, held in the highest esteem ; and the third might have 
been named in allusion to the twin season of their flocks. 

723. In this manner was parcelled out the Zodiac into twelve 
parts or signs, each sign spread over thirty degrees of the heav- 
ens, or the twelfth part of three hundred and sixty degrees. 

724. This division of the Zodiac into twelve parts was arbitrary ; 
and although the constellations have somewhat changed their 
places during the lapse of so many centuries the signs still remain 
in the same order as numbered by the Chaldean shepherds ; but 
the signs do not answer to the same points ; and the stars, which 
were then in conjunction with the sun when he was in the equinox 
are now a whole sign, or thirty degrees, to the eastward of it ; so 
that the first star of Aries is now in the portion of the ecliptic cal- 
led Taurus ; and the stars of Taurus are now in Gemini, and those 
of Gemini in Cancer, and so on. By this retrograde motion, the 
pole, the solstices, the equinoxes, and all the other points of the 
ecliptic, have a retrograde motion, and are constantly moving 
from east to west, or from Aries towards Pisces, at the rate of 
about fifty seconds and a quarter each year, which is called the 
precession of the equinoxes. This rate of retrograde motion being 
constant, it will require twenty-five thousand seven hundred and 
ninety-one years for the equinoxes to make their revolutions west- 
ward quite around the circle, and return to the same point again. 

725. In June the sun enters the 4th sign, Cancer, (the crab.) 
Here he ceases to advance northward, but begins to go back to- 
wards the equator. This retrograde motion might have suggested 
the name of an animal which is said to move by going backwards. 
In July the sun enters the fifth sign, Leo (the lion ;) at which time 
the heat of the sun was lion-like, that is, strongest and fiercest over 
the regions of Chaldea and Egypt. The sixth sign is Virgo, (the 
virgin,) represented as a female reaper. The sun enters this sign 
in August, the harvest month. In September when the sun is in 
the sign Libra, (the balance,) the days and nights being equal, 
balance each other. This is the seventh sign. The s,un enters 
the eighth sign, Scorpio, (the scorpion,) in October, when the au- 
tumnal fruits having engendered diseases, the season may be com- 
pared to the poisonous reptile which bears a sting in his tail. In 
November the sun enters the ninth constellation, represented by 
Sagittarius, (the archer.) The season when beasts of the chase 
are in flesh, and when men take delight in hunting. The tenth 
sign of the Zodiac, Capricornus, (the goat,) is the emblem of the 

723. Twelve signs. 

724. Precession of the equinoxes. 

725. When is the snn in Cancer? Leo? Virgo? Libra? Scorpio? 
Sagittarius 1 Capricornus ? Aquarius 1 Fisces ? 



CONSTELLATIONS. 



293 



winter solstice, when the sun turns about, as it were, and, from 
(he southern tropic, begins to climb towards the equator. The sun 
is in this sign, six months after he has, like the crab, began his 
retrograde motion from the sign or tropic of Cancer. The eleventh 
constellation on the Zodiac, is named Aquarius, (the water bear- 
er.) It is represented by the figure of an old man in the act of 
emptying an urn of water. The season of humidity, fast hastening 
to its close. In February the sun rises with the constellation 
Pisces (the two fishes ;) indicating the fishing season, when the 
earth is bound in frost, the seas offer their stores for the sustenance 
of man. This is the twelfth sign of the Zodiac, and closes that 
great circle of the heavens. 

720. When the earth is in that part of her orbit represented in 
the figure at a, a right line from the earth to the sun, and extend- 
ed to the fixed stars, would pass through the sign Libra, thus the 
sun would appear as if situated in that constellation. When the 
earth is at b, the sun will appear to be in the sign Capricornus. 



Virgo. 1rtq 



Libra. 




Taurus 



T Aries. 



Scorpio. Yft 

Sagittarius 



Piscei 



Capricornus. 



727. Besides the twelve constellations of the Zodiac, there are 
reckoned about thirty-five constellations in the hemisphere north 
of that plane, and forty-five south of it. 

The Little Bear, (ursa minor,) is a constellation situated near 
the north pole of the heavens ; from its being almost at the axis 
of motion, it scarcely has any revolution, and always appears 

726. Explain what is meant by the sun being in any constellation. 

727. Number of constellations besides those of the Zodiac. Ursa minor. 
Polar star. Arcturus with his sons. Mazzaroth. 

25* 



294 



NATURAL PHILOSOPHY. 



above the horizon. In the tail of this constellation is the North 
Star, sometimes called the polar star. It is a star of the third 
magnitude, and not remarkably brilliant. 

The polar star is easily found by its being in the neighborhood 
of the constellation known commonly as the Dipper, (the Great 
Bear, or Ursa Major.) In this constellation, four bright stars in 
the body of the bear form the bowl, and the three in the tail form 
the handle. There are two stars opposite the handle of the Dip- 
per, called the pointers, because they always point to the north 
pole of the heavens, from which the polar star is nearly two de- 
grees distant. Several degrees west of the Dipper is a bright star 
of the first magnitude called Arcturus ; it is in the constellation 
Bootes, or the Bear Driver, so called because it seems to be pur- 
suing the Great Bear around the pole. " Canst thou guide Arc- 
turus with his sons, or bring forth Mazzaroth in his season ?" in- 
quired the Most High of Job. Arcturus, being the leading star 
of Bootes, seems here to refer to the whole constellation. Mazza- 

Fig. 282. 
North Pole of the Heavens. 




rolh is supposed to be a general term for the constellations of the 
Zodiac, which, by being brought forth in their respective months, 
cause the varieties peculiar to the different seasons. 

728. No young person should remain ignorant of the names and 
places of the most remarkable constellations and stars. It is as 
easy to find the place of Orion in the heavens, as it would be a* 
Rome to find the situation of St. Peter's church ; and as for " The 
Dipper," there are few children who have not had it pointed out 
to them. That brilliant star of the first magnitude, situated south 
and east of Orion, in the constellation of the Great Dog, called 
Sirius, or the Dog star, is always viewed with pleasure and delight, 
even by the vulgar and uninstructed. This beautiful star, although 

728. Study of the constellations easy and pleasant. 



NEBUX^. 295 

not often scon by us except in winter, is, in reality, over our heads 
during the day in mid-summer, rising with the sun during a month, 
from the 24th of July to the 24th of August. The heat, which is 
usually most oppressive at this season, was formerly ascribed to 
the conjunction of this star with the sun. And the distinctive 
name H Dog days," is still given to this season. 

729. The Milky Way, or Galaxy, is a luminous zone in the 
heavens, of a dazzling whiteness. It was long a question with 
astronomers what occasioned this broad arch of light across the 
sky. But at length Sir William Herschel, aided by his great 
telescope, proved that this brightness was the combined effect of 
myriads of stars, so distant that their image is lost to us. This 
celebrated astronomer counted not less than fifty thousand stars, 
which passed through the Held of his telescope in a zone of the 
heavens two degrees broad. 

730. Nebulce, are spots in the heavens, which even with ordi- 
nary telescopes, appear but as white clouds, or masses of unform- 
ed light. When examined by the best telescopes, they give the 
idea of a concave space filled with stars, insulated in the heavens, 
and constituting systems of their own. "To attempt to count the 
stars," says Herschel, " would be hopeless ;" but he thinks many 
clusters of this description contain no less than twenty thousand 
stars, compacted into a space not one tenth as large as the moon's 
apparent surface. "If each of these stars," says Mrs. Somerville, 
" be a sun, and if they be separated by intervals equal to that which 
separates our sun from the nearest fixed stars, the distance which 
renders the whole cluster scarcely visible to the naked eye, must 
be so great, that the existence of this splendid assemblage can only 
be known to us by light which must have left it at least a thou- 
sand years ago. 

731. The study of the starry heavens is an elevating and noble 
pursuit, introducing us to a knowledge of God, in the contempla- 
tion of his most sublime and glorious works. From the earliest 
periods of time it has added warmth to devotion, and to poetry its 
happiest inspirations : Thus Euripides, the Greek poet, in his 
drama of Ion : 

Meanwhile the Night, robed in her sable stole, 
Her uurein'd car advances ; on her state 
The stars attend ; the Pleiades mounting high, 
And with his glittering sword Orion arm'd ; 
Above, Arctnrus to the golden pole 
Inclines; full-orbed the month-dividing moon 
Takes her bright station, and the Hyades 
Marked by the sailor. 



729. Galaxy. 

733. Nebulae. Opinion of Herschel. Remarks of Ivlrs. Suxnervilk 

731. Observations upon the aludy ^f the heavens. 






296 NATURAL PHILOSOPHY. 



732. Having indulged imagination in wandering through the 
solar system, and the more remote regions of space, as far as the 
human intellect has yet dared to penetrate, we must now return to 
our own little planet. The earth, indeed, appears insignificant 
when considered in relation to this vast universe, and even to the 
system of which it forms a part. Among the family of worlds 
which move around the common center of attraction in the solar 
system, our planet is but an inconsiderable member. If Mars and 
Mercury are of less magnitude, the far distant Herschel, with his 
numerous satellites, Saturn with his splendid rings, and attendant 
moons, and the magnificent Jupiter with his retinue of worlds, all 
fill a far greater extent of space, and must offer to the view of a ' 
spectator situated in some central point, an appearance far more 
grand and imposing than earth with her diminutive size, and the one 
little ball revolving around her. Let us learn a moral lesson from 
the stars ; — we see that God has not made them all alike, but "that 
one star differeth from another star in glory," yet each harmoniously 
fulfils its destined round in the economy of nature. So it is with us, 
the beings who inhabit the little planet, called earth. Some have 
more wealth than others, some have greater intellectual power, 
some are lifted up, and some cast down ; but all should harmoni- 
ously move on in their assigned orbits, trusting that he who placed 
them there, knows best how to order his own creation. And. 
again, there are always some compensations, which may be set off; 
against disadvantages — thus the earth, though not great like Jupiter,/ 1 , 
nor like him followed by a train of attendants, is favored with more 
warmth and light, as the lowly man is often peculiarly favored witl 
spiritual enjoyments, and the light of God's countenance. 

733. But our connection with the earth we now inhabit, is to be 
of short duration ; — we may move upon it for a little while, and 
then our ashes will repose in its bosom until that day, " when the ] 
heavens will be rolled together as a scroll, and the earth shall melt 
with fervent heat." Under new and glorious forms, we shall then 
be translated to regions free from sin and sorrow ; our celestiaH 
bodies v/iil have power to range through the infinity of creationlj 
and our souls will be delighted with the contemplation of glories/ji' 
which mortal eye hath not seen. But that we may be thus happyJ| 
thus blessed, we must here cultivate the better faculties of our na- 
ture, and make our intellectual attainments subservient to moral ji 
elevation. The rays cf science, collected into a focus by religion,^ 
and directed towards the heart, cannot fail to warm and animate ioj 
with new love towards God, the Father of our spirits and them 
Author of Nature. 

732. The earth compared with other heavenly bodu-s. 

733. Conclusion. 

THE END. 



